While things still aren’t totally clear when it comes to purchasing games on Stadia, Google did clear things up a bit with a new FAQ that they published a few days ago.
Specifically, their info reads:
What happens to a game I bought if the publisher stops supporting Stadia in the future? Can I still play the game?
Yes. Once you purchase the game, you own the right to play it. In the future, it is possible that some games may no longer be available for new purchases, but existing players will still be able to play the game. Outside of unforeseen circumstances, Stadia will aim to keep any previously purchased title available for gameplay.
That’s essentially what we expected, but it’s good to hear it directly from Google. Check out their full FAQ for answers to other questions that you might have.