It depends what "stops working" means? I have an old Mac where Steam isn't officially supported anymore, but I can still run all the games that I installed on it. The Steam client simply stopped updating and the last version that worked still works fine. Put the Steam client in offline mode and it works.

Or you mean Valve shutting down Steam? Then yes, it could be a problem for some games that use Steam servers for online multiplayer. But, Steam is Valve's core business with proven track record and many loyal customers. It's much more likely that Stadia would shut down then Steam going away.