I imagine you are getting down votes because your second paragraph:
Also, universe is explosively expanding. It's almost impossible that the star remains will come close enough to form new stars. (Although, they can't if it only has heavier elements). So, no, stardust can't give rise to new stars.
is not correct. Stellar remains are, in fact, a significant contributor to the composition of new stars. They make up a small but very important part of the mass. (Moreover, while the universe is expanding on extragalactic scales, the interiors of galaxies, where stars are located, are not expanding.)
A wrong answer is probably the best reason to down vote something. So there is no reason to see anything inappropriate going on here.