What would need to happen for a single woman's mitochondrial genome to be in all living humans ?
All other women would suddenly or gradually need to be eliminated from the gene pool. No other woman could enter the gene pool of this future humanity. So the most likely scenario is one where we would have to be reduced to a single woman at some point.
Genetic isolation was brought up, but the words 'all living humans' doesn't really say 'isolation'. In isolation, there are other people still carrying on somewhere else. Here we are talking about only isolation in the sense that the breeders are the only ones left to reproduce.
Even so, any human woman will still be descended from MEve. That original Eve would still be the mitochondrial Eve, though the genomic record pointing to her would have disappeared.
A completely New Eve could happen if there were a woman unrelated to MEve were to come along, and her offspring were so much more successful than all other women that over time only this woman's daughters were chosen as mothers. She would be incredibly successful- like all her children were 6'6" and much smarter, attractive etc etc, then the rest of the gene pool could dwindle leaving only 'new Eve'. This could happen say if we got some Neanderthals going. They don't seem to be particularly likely to take over though.
This is similar to the scenario where one female lineage simply out-competes all other female lineages to assume the mantle of M-Eve. This seems less likely to me. This lineage would have to enjoy an advantage would have to out-weigh all over variants that exist at the time and would ever emerge over the following generations before our new M-Eve's final domination. Given the number of genes and possible variants, in the entire genome, that is statistically really improbable.
As far as a new Y Adam, this sort of thing nearly happened for men. Just to remind, the Y chromosome is transmitted exclusively from father to son, so a Y Adam would be the only ancestor of all men on the face of the planet.
A national geographic sponsored survey of genomes found that in central asia 8% of all men have the same Y chromosome. Over all humanity, 0.5% of all men have the same Y chromosome. The genetics point to the Mongol Warrior King, Genghis Khan whose campaigns across Asia to the doorstep of Europe included him bedding with one or more different women from the conquered peoples every night, one of whom is reputed to have killed him. Not incidentally killing many men too, eliminating much future competition for his progeny.
Still, all this is a mere fraction of the sort of effect you are talking about. 100% replacement by a single individuals descendants is hard to imagine in less than an extinction like scenario. Or a new race of superbeings coming from a single individual. Hard to imagine given the billions of people on the face of the planet now.
Its a little easier to imagine in the case of a new Adam only because a one man can have hundreds or even thousands of offspring in his lifetime. Even then, Male psychology seems to bring it up more than is rational. Its still extremely improbable (not going to happen).
Its also worth noting that few species have been able to come back from such a small gene pool and number...
Here's a tree of human Y chromosomes. You can see that fat grey blob which are descendants of GK.