At least one game created in the Soviet Union has been the cause of dozens of cease-and-desist orders, lawsuits, and indie games being shut down.
In other words: Yes, or at least most likely.
Technically, if an entity (a state or a company) ceases to exist, it has no more rights, but in almost every case there is a heir at law to the entity. Which means no more and no less that someone else takes over the same rights. Or, the same person(s) that held the laws previously keep them under somewhat different (or identical) conditions or a similar (or identical) name, i.e. a "Soviet" claim might simply become a "Russian Federation" claim.
Also, trademarks may be acquired in other locations independently.