How do Playstation Plus games work?

If you get a free game from your PlayStation Plus membership, it will be tied to your account.

You can add these titles to your library without actually downloading them at that time.

If the PS+ account is the primary account for the console, yes, all other users on that console have access to the game. If your PS+ account is not the primary account for the console, then only that account will have access to your games.

As others have mentioned, if you let your subscription end, you will lose access to the games you were given for free. However, I believe that they are still tied to your account, so if you renew your membership, you will regain access to those titles.