I mean, Hemocytoblast is a stem cell which is constantly being differentiated into daughter cells and leads to formation of all the blood cells (having short and limited life spans), so how come those stem cells remain there and continue to function, even when we grow up and finally grow old (i.e for 70 years approx)? The no. of those stem cells gotta be limited.
The trick for the stem cells lies in the way the proliferate and differentiate. See the image (from the reference 1):
Stem cells have the problem that they need to differentiate and maintain their population at the same time (subfigure a). This can either be done by asymmetric cell division which leads to one daughter which is still a stem cell and one which has been differentiated (subfigure b). Then it is possible that the cells divide only symmetrical (as shown in subfigure c) so they will either deliver two stem cells or two differentiated cells. And then it is possible (shown in subfigure d) that both possibilities are mixed and that symmetrical and assymetrical division occurs. Either way you get both: Differentiated cells and you still manage to maintain the stem cell pool.