Every MMO does some kind of compute or validation on a server. Sim City was supposed to use something similar, at least if we are to believe the developers. However, they fell incredibly short of using internet connections to actually expand the game.
Yes, a company can shut down a server that is required for a single player game. However, the scaling of costs with the scaling of servers makes it a lot less likely. Will it happen eventually? Well, of course. It isn't like they have to devote a ton of resources for older games now though. They can have one VM running a single server instance that can accommodate the few players still playing.
If a company does decide to go the OnLive route, then it would take a lot more resources to keep the game running, but after that huge failure, I don't see it happening. However, nVidia shield is doing something similar, so who knows.