A game subscription feels like owning a huge library. Mostly it isn't. It is closer to a library card: it works while it is active, and the books go back when it stops. Knowing which parts you keep and which you lose makes it much easier to decide when to subscribe, when to pause and when to buy a game outright.
Think of your account as three shelves. The first holds subscription games: the catalog titles you can download and play while you pay. The second holds games you bought. The third holds your progress: saves, achievements and trophies.
On Xbox Game Pass, catalog games check your subscription every time you launch them. If the subscription has ended, that check fails and the game won't start, even if it is still installed on your drive. On PlayStation Plus, the same idea applies to the monthly games and catalog games you added: PlayStation says that content downloaded at no cost as part of the subscription is no longer available once the subscription ends. Games you paid for are not affected on either platform.
Games you bought stay yours, including ones you bought at a member discount. Many platforms also keep your achievements and trophies on your account, and save data generally comes back if you resubscribe or buy the game later. Cloud storage rules differ by platform and can change, so before you cancel, check your platform's current terms if you care about a specific save.
The one thing to remember: a subscription rents you access to games, it doesn't sell you the games.
Catalogs rotate. Games arrive and leave every few weeks, and platforms often show a "leaving soon" list. Members also tend to get a discount on buying a game that is about to leave, so a rental can turn into a purchase if you love it. If a game on that list is one you would replay for years, buying it can be cheaper than resubscribing later.
Subscribe when you want to try lots of games and finish most of them within a few months. Buy when it is one game you will keep returning to. Pausing between big releases is a normal way to use a subscription, because your saves and trophies are not what you lose.
Also check what your subscription includes besides the library. On most consoles, online multiplayer and cloud saves are tied to a different tier, so cancelling can affect those too.
Look at the leaving-soon list and buy anything you will replay. Finish games you are mid-way through, or note where you stopped. Check your platform's page for what happens to cloud saves and extras like monthly games. Then cancel, knowing you can come back later.