There's a community of Confederate descendants in Brazil. Most of them have assimilated but a few live in ancestral lands. There's an annual festival and everything.
https://en.wikipedia.org/wiki/Confederados
https://www.vice.com/en_us/article/welcome-to-americana-braz...
There were also settlements in Belize and Mexico apparently. None of them lay claim to being independent nations and owning mainland US though.
The ROC as I see it retreated into an enclave of the former whole China and was never fully vanquished from Chinese land. So it's really more like if the Union stopped fighting after the Confederacy was defeated in all but one breakaway state. Even more accurately, since the PRC were the rebels, it'd be like the Confederates took over all the Union states except, say, Pennsylvania and then the war came to a halt. The Pennsylvania redoubt of the US would still be the US and may or may not make claims to the rest of the formerly united United States.
But what do I know about the situation? I'm just an American.