I've said this like a thousand times and I hate repitition, but the USA as a whole has never tried to ban TikTok. Trump claims he did, it isn't allowed for military servicemembers, but it has never been banned.
Forced sale only works if your government has any control over the organizational structure of your company which the USA does not. What they are effectively doing is forcing the American arm of Tik Tok to sell without access to it's technology which China can absolutely deny. If the sale doesn't go through, the US will ban its use. If they do sell, it will be without the technology and a company will be Tik Tok in name only having to essentially build the service from the ground up. This is an effective ban of Tik Tok regardless of the outcome.
What makes you think the proprietary rights held by the Chinese hold any sway in the USA? If they want to try suing they can, heck they can even take it to international courts, but they won't have much luck given the evidence that China was using it maliciously.
What I mean is, there is no way the Chinese headquarters of tik Tok will let the America arm of the company have access to its algorithm. Tik Tok is nothing without its algorithm. At best it's a large install base that will dwindle once they realize til Tok kinda sucks all of a sudden.
Oh that would be interesting, it seems very uneconomic for it to be that centralized because the US facilities would be useless but I suppose I could see it as a possibility. In that case, whoever they sell to could try to sue them with pretty unlikely odds of success. More likely China would just refuse to sell in that circumstance, in which case it would be the same as China themselves ending TikTok.