What happens to clones a deepspawn created if/when the deepspawn dies? (D&D mechanics and/or lore)

I am running a 5E homebrew campaign where a powerful creature akin to a deepspawn is consuming and creating spawn of powerful beings in various governments and organizations to puppet a growing portion of civilization.

My question is should my players succeed in finding and destroying this creature, what have past editions and/or D&D literature said about the fate of the spawn it had created?

Since this is homebrew I know I can pretty much do whatever I want, but I’m looking for insights into how to handle it so I have a plan in place.

I only have access to the Lost Empires of Faerun 4E book regarding them, and though it goes into detail about how the spawn are created and what the spawns’ capabilities are, it does not mention anything about the spawns’ existence after the deepspawn is slain.

Any examples from D&D literature or rulebooks would be greatly appreciated.