If Earth broke apart several large chunks, could life continue on said chunks?

So I recently learned about the theories of the moon’s origin. One being that a Mars like body named Theia impacted Earth, causing pieces off Earth to break off. One of which became the moon.

But this was before we were around. So if we had a repeat and a populated piece of Earth broken off and was thrown into orbit, if some were to survive the initial impact, would they be able to continue life on their newly formed home?

And if no, would there be any way to make it habitable?