Janeway's does not seem to explicitely answer your question:
A. "T cells that cannot recognize the body's own MHC molecules (...) this process of positive selection (...)"
B. "Lymphocytes whose receptors bind strongly to self antigens, on the other hand, receive signals that lead to their death; this is termed negative selection."
Your question refers to T cells that recognize foreign MHC. In fact, Janeway's does not seem to cover that situation relevant for transplantation of "allografts".
This suggests that general principles do apply:
A. Lymphocytes that do not recognize self MHC may still recognize foreign MHC.
Janeway's quote "T cells that cannot recognize the body's own MHC molecules" - does not exclude that there are T cells reacting to foreign MHC. They would not enter the process of selection and would not be "sorted out". Your question, literally, "where do they come from" thus seems a rhetoric way to wonder a. how their existence can be taken for granted (in literature) and/or b. how it can possibly be that they have not been sorted out and died of neglect because of non binding to self MHC.
Two quotes to a. above:
From Trends in Immunology, 2016:
"Alloreactive T cells include those that recognize intact donor MHC molecules on the surface of donor cells – referred to in transplantation as the direct pathway of allorecognition – and of peptides derived from polymorphic regions of the allogeneic MHC molecules or of non-MHC proteins presented by self-MHC molecules, which is known as the indirect pathway."
Marino et al., "Allospecific T cells become activated through interaction of their T cell receptors with intact allogeneic major histocompatibility complex (MHC) molecules on donor cells (direct pathway) and/or donor peptides presented by self-MHC molecules on recipient antigen-presenting cells (APCs) (indirect pathway)".
There is no need of "presentation" on APC cell's MHC in "direct pathway". It seems consistent with the definitions quoted above to assume the existence of allo-aggressive T cells (derived from regular lymphogenic stem cells) not binding to self MHC, thus not entering any process of "death by neglect". Put more bluntly: no fostering needed for those to remain.
Random google found this:
J J Ryan et al.(Recognition and response to alloantigens in vivo. I. Negative and positive selection ...):
"This finding may implicate other sites such as the liver where unprimed host alloreactive clones are trapped."
In that passage, if you read "unprimed" as "never got acquaninted with antigen", that quote will appear supporting the view that allo-MHC-binding T cells exist and have not been sorted out, and needed no fostering.
See also Distler et al. "Alloreactive and leukemia-reactive T cells are preferentially derived from naïve precursors in healthy donors..." Title of paper seems to respond to your formulation "...where do they come from?"
See also "Between 0.1% and 10% of naive T cells within an individual are estimated to be reactive with any unique allogeneic MHC haplotype." with further reference, Brehm et al., Rapid quantification of naive alloreactive T cells...
Emphasis in quote to be set on "naive", which might misleadingly be understood as: not having undergone positive or negative selection. I refer on my elaboration on distinguishing "selection" and "presentation"(priming) in the very last part of my answer (more learnt then). In any case, those T cells exist and have not died.
The fact that there is "direct pathway" lays proof that, conversely, any "fostering" (survival signal) is not needed for allo-aggressive lymphocytes becoming "activated through interaction of their T cell receptors with intact allogeneic major histocompatibility complex (MHC) molecules", see quote above.
B. Refering to the "indirect pathway" and "negative selection" (this is even more intricate, to my mind...), the sorting out of T-cells which react to their specific antigen on self MHC seems to eliminate any cell reacting to that same specific antigen presented on foreign MHC by transplant cells. This is a fallacy.
Indeed, there cannot be any presentation of foreign antigen (of transplant cells) on self APCs if, by negative selection, those specific T cells have been sorted out. Those T cells do not exist any more.
However, the specifity of the T cell receptor is defined by a duality of signals, by the combination of MHC and antigen. The term "MHC restriction" might be misleading in that context. "Restriction" means that there need to be two signals, not just one or the other. Then,second, specifity of the T cell receptor has been found being defined by the duality of those two signals. There is only one T-cell receptor, no two
(There is some related question at stackexchange concering "super antigens": certain antigens on certain MHC alleles - however, question of "super antigens" does not refer to the difference between iso- and allo- (transplant) antigen.)
Thus, T cells that bind to the combination of self MHC plus antigen (possibility to immunize against transplant by presentation on self APC's MHC) may also, at the same time, react to foreign MHC presenting that same antigen. "MHC restriction" does not rule out "homology" of T cell receptor specifity (for better understanding: antigen, not iso-/allo-MHC "determines")
To sum up, applying general principles,
a. there may be t cells recognizing foreign, not self MHC, which in lack of any binding have not received any "death signal" (cp. quote Janeway's above) and have not been sorted out by positive selection ("direct pathway").
b. negative selection does not eliminate t cells that bind antigen presented on foreign MHC, which is consistent with duality of signal specifity of T cell receptor thus defined by a combination of MHC and antigen ("indirect pathway").
By the way, you say: "T cells which present antigens on self-MHC are selected positively..."
That should read: "T cells that react to antigens being presented on self-MHC (by APC, not t cells)..."
There is a some other question on stackexchange very much related to yours:
Understanding transplant rejection - how does the cellular, adaptive, response get underway
This question shows that it is not at all trivial to assume the existence of T cells taking foreign MHC as foreign antigen. See quote at the very end of my answer.
Your question is a valid, my answer very much a personal one,
"Alloreactivity, defined as a strong primary T cell response against allelic variants of major histocompatibility complex (MHC) molecules in the species, has been a long-standing puzzle in immunology with some of its details remaining unclear up to now" (Nagy 2012)
Counterintuitively, "positive" selection, more than negative, might be the big exception to some rule that prohibits autoagressive killing of self MHC cells. Conversely, to attack cells carrying foreign MHC might be the "general principle" that needs no explanation (Interestingly, T cells are said to - in some cases - be activated by cytokines alone (interferon); interestingly, to find foreign MHC in the blood is no natural situation for human t cells - in that way, transplantation seems to imitate evolution).
Finally, here is some lengthy quote:
"Paradoxically, while T cells that obtain too strong signals from self-pMHC are removed, those T cells that survive and complete their developmental program require a productive, weaker, signal from interaction with self-pMHC to do so. T cells incapable of such signaling die by ‘neglect’ and this requirement for a survival signal from TCR recognition of self-pMHC is known as positive selection. While the experimental evidence for positive selection is overwhelming, just what this process contributes to a useful T cell repertoire has been hard to establish.", Vrisekoop et al. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4152861/
Your question seems to pertain to "death by neglect" of T cells able to respond to foreign MHC (of transplants). "Neglect" might denote nothing more than lack of survival signals; conversely only those lymphocytes able to become cytotoxic, i.e. autoaggressive, "contribute to a useful T cell repertoire", as any anergic T cell is no (self-!)cytotoxic killer cell which is the needed function. On the other hand, quote, "T cells that obtain too strong signals from self-pMHC are removed..." speaks in favour of MHC being recognized by lymphocytes basically as some antigen like any other: as there are T cells that attack foreign MHC there do exist - counterpart - T cells that react to self MHC even when there is no presentation of antigen. These cells, in my understanding, "obtain too strong signals from self-pMHC" and "are removed". Negative selection discards T cells that react to self MHC if there is antigen presentation. This process does not imply the sorting out of T cells reacting to foreign MHC alone.
Cp. answer to another related question here on Stackexchange: "Why do physicians try to match HLA complexes for organ transplant?" (...)
To quote one answer: "In short, if a T cell does not find its corresponding MHC 1 complex on a particular cell, its default behavior will be to attack it." There is no contradiction to this statement assuming that foreign, non self MHC1 is the antigen the allo-aggressive T cell is "specific"; MHC1 is to be considered "antigen" (it is known that peptide parts of foreign MHC are presented on host MHC - "imagine" MHC presented on MHC...).
See comment to quote by User inf3rno:
"Regular T-cells (without NK receptor) seem(...) like having the same ability by not compatible MHC1, but I am not sure yet about the mechanism. I think I'll need a (week) more to read all articles I opened and come to a conclusion about how the immune response works in this case."
Let me add one last quote I came across doing further research:
"...the closer the foreign MHC molecule is related to the T cell's MHC, the higher is the proportion of peptide-specific, alloreactive (“allorestricted”) T cells versus T cells recognizing the foreign MHC molecule without regard to the peptide in the groove. Thus, the peptide repertoire of alloreactive T cells must be influenced by self-MHC molecules during positive or negative thymic selection or peripheral survival, much like the repertoire of the self-restricted T cells. In consequence, allorestricted, peptide-specific T cells (that are of interest for clinical applications) are easier to obtain if T cells and target cells express related MHC molecules.", Obst et al., The Role of Peptides in T Cell Alloreactivity Is Determined by Self–Major Histocompatibility Complex Molecules
First, the formulation "T cells express MHC" bears similarity to the wording of your question "T cells presenting antigen on their MHC" which I denounced as incorrect up above, "by the way..."
Second, I find this quotation consistent with my summing up my answer as follows:
There are a. naive T cells derived from regular stem cells that are solely allo-MHC-reactive and thus have not entered any selection process (they "just survive", direct pathway), there are b. (more intricate, indirect pathway) T cells prone to self MHC having survived selection/tolerization process that not only bind self, but also bind foreign MHC presenting antigen which there has been no tolerization for.
Let me add one quote that speaks against my answer, point A, concerning the existence of allo-aggressive T cells (for illustration's sake: "in peripheral niches") that have not bound to self MHC and thus have not been sorted out:
"Crossreactivity seems to be an intrinsic property of the TCR required, because a single TCR must possess the ability to interact with both self-MHC during positive selection and at least one combination of foreign antigenic peptide presented by self-MHC. Recognition of allogeneic MHC molecules is an inadvertent consequence of the need for TCR crossreactivity." quoted from: The structural basis of T-cell allorecognition, A Whitelegg 1, L D Barber, 2004
This refers to any T cell in need of "survival signals". My answer, point A., argues that during positive selection non- (to modify my answer: too weakly) binding lymphocytes remain non fostered which does not lead to their vanishing (only non tolerant lymphocytes to receive "death signals").
On the other hand, this quote speaks in favour of point B ("more intricate", see above): T cells that tolerate self antigen might, by "cross-reactiviy", become cytotoxic when presented same antigen on foreign, non self MHC of allograft.
Your question - there are related ones on Stackexchange - turnes out to be some exiting one. Point A, above, is basis for debate. Here is some empirical study, corroborating my point of view: it is "not natural" for T cells to attack cells of their "own body" (self MHC). The point of "positive" selection, i.e. "nurtering" is, to find auto-aggressive T cells, or even T cells that bind to self MHC. Thus, it becomes natural that T cells that bind - aggressively - to foreign MHC survive non binding self MHC. Positive selection searches for auto-immunity (self MHC cells infected by virus, cancer cells shall be bound to); there is no natural counterpart in the negative.
Here's the quote:
"These findings suggested that the clones recognized determinants on H-2Kb that were independent of peptide.", P A Smith, Brunmarck, Potter, Peptide-independent recognition by alloreactive cytotoxic T lymphocytes (CTL), 1997
This was from 97. More and more as time goes by, from 2017, encore:
"NKT cells—originally defined as cells that co-express key natural killer (NK) cell surface markers and a conserved αβ TCR repertoire—are thymus-derived, innate-like T lymphocytes. The functions of NKT cells are controlled by self and non-self-lipid agonists presented by CD1d molecules.." from: Natural Killer T Cells: An Ecological Evolutionary Developmental Biology Perspective, Amrendra Kumar et al.
Some reference that speaks against subsets of T cells acting like NK cells would be Uzhachenko an Shanker (e.g.) say:
"By contrast, NK cells lack antigen-specific receptors but express (...) inhibitory and activating receptors that bind various ligands including MHC and like molecules. A highly calibrated maturation enables NK cells to eliminate target cells with lowered or absent MHC-I or induced MHC-I-related molecules while maintaining their tolerance toward self-MHC
It seems some open question if there is a full spectrum that fills the gap between T cells that undergo positve, negative selection and Natural Killer cells that just do not (but need maturation). As I understand quote from 1997 above those T cells may need presentation of MHC antigen to become alloaggressive. Now, trying to explain in a fast, illustrative way: Corresponding to presentation of foreign MHC peptide on self MHC there should be foreign MHC peptide presented on foreign MHC of the allograft cells to attract the activated Tc cells. However, presentation of graft MHC as antigen on foreign graft MHC just does not exist, does not seem to make sense. Why should the allograft cell present its own MHC on its own MHC? How do host T cells "come on" then?
So the "priming" in that case of "transplants" very much appears as a process of clone expansion. I think it is very surprising to see the "fostering by non neglect" in "positive selection" as a very early priming (not even sure, it's seldom heard I guess to speak of "priming" when dendrite present antigen as APC in lymph nodes) of sought of "rare" - according to my view - potentially self-aggressive self T cells. It's coherent with literature to assume that there are T cells entering "late positive selection" which is nothing else than being presented with foreign MHC peptides - in that case of transplants - by self APCs (or foreign APCs, by the way, no difference).
One more quote to this, from 1991:
"The high determinant hypothesis emphasized the implication of direct contact between the T cell receptor and the MHC molecule; the multiple binary complex hypothesis envisages that alloreactive T cells are specific for self peptide bound by the foreign MHC molecule." From: The molecular basis of allorecognition of major histocompatibility complex molecules by T lymphocytes, G Lombardi 1, R Lechler
It's a possibility that - according to a basic underlying principle - there are groups of T cells that react cytotoxically to foreign MHC cells without those presenting any peptide - as they bind to foreign, not self, MHC. No sorting out for "NK T cells" (as NK cells).
To end up I'd like to illustrate: a memo square in "Immunology for dummies", German version, states: for graft rejection to occur there must be antigen presenting cells of the host, and this needed no explanation. How could cells presenting on host MHC even contact graft lymphocytes if graft's presenting cell had eliminated any lymphycyte that "does not recognize graft's MHC" in the sense: hence, recognizes any future host's MHC? This is paraphrasing your question and showing why it is a valid one.
To sum up my answer:
In positve selection, there is presentation of antigen; lymphocytes with low affinity to self MHC ("MHC restriction" must not be taken for "restriction to self MHC, it means combined, dual signal) will not be fostered.
In negative selection, there is presentation of self antigen (paralleled: not only antigen, as in positive selection there is not only MHC); lymphcytes with low affinity to self-antigen - are not killed (reverse parallel: in positive selection lymphocytes with low affinity to self-MHC are not killed; this is difficult to find reference, see above).
My hint from a learner's perspective:
Basis is "cross-reactivity" made possible by "MHC restriction" which does not mean restriction to self MHC, but does mean "homology" of dual signals.
When reading about positive selection try to "catch the eye": is there antigen presentation (or "showing self-MHC" and sorting out only, misleading).
When reading about negative selection have an eye on lymphocytes surviving because of their "low affinity" to: antigen (or is there sorting out only of antigen avid lymphocytes, misleading).