Is any game you pay for yours forever or does it expire with your Gold pass?

Good day

As the others have stated.

You own the game if you paid for it.

If you actually pay for a game, it's yours. If you download the 360 Games with Gold games, they are yours. The One Games with Gold games require that you keep a gold subscription in order to continue playing them for free.

Well, if you get the Xbox 360 games, they are forever free to own to download later, even without Gold, but Xbox One, those will not be free if Gold expires.

To clarify, if you pay for a game (even with a Gold member discount) you own the license in perpetuity. If you claim a 'free' Games with Gold title you own it in perpetuity. If you play a game on Game Pass and don't buy it, you don't own it.

If you PAY for the game then its yours. Even if you get a discount using Game Pass or Gold. But if you just get the game because of Game pass, you can only play it as long as you have an active Game pass Subscription and the game is
still available on the service.

If you get a Free Games with Gold Game, The Xbox one games are only playable as long as you have a valid Gold Subscription.

Hope that helps