So, I know Vernor Vinge mentions Earth in his books, but I don't think they specifically mention what happens to Earth. Does anyone know?
In chapter 37 I found:
Old Earth had been depopulated four times. Without the existence of the daughter worlds, the human race would have gone extinct there long ago. What lived on Earth was strange now. None of their kind had been this far out from the center of Human Space before. But now, as fleets made their final approach into the Namqem system, the Old Earth ships were barely ten light-seconds from Pham’s flag.
So Earth is still populated, and I think by humans. However I can't find any more about the ships from Earth or what made them strange.
If memory serves, there's also a moment where Pham is communicating with the Old Earth fleet commander over video (or its far-future equivalent) during the Namqem operation, and he's described as being only nominally human... or an 'it'.
Since the Slow Zone prohibits Singularity-level technology, I took this to mean that the current resettlers of Old Earth had extensively modified themselves (surgically, genetically, cybernetically, etc.) to live in its current environment. Of course, it could also mean perhaps they're part of an exotic religious/philosophical order, and that those are their badges of distinction... or any number of other explanations not tied down to issues of survival.