The company owns the whole characters but yes, they usually reach a level of popularity where, even without explicitly stating it before leaving, they can just start streaming independently with a different character and a good chunk of the fanbase will still find and follow them again.

The company doesn’t even seem to be against it actually, and afaik one time where they had to terminate a talent for breach of contract, they pretty much encouraged her to start streaming again as an indie and wished her good luck.