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At some point, you break the game.
If you have a game with levels, however, it's just bad design to let those levels continue infinitely. Most games don't offer this, because they've learned from ... like, pacman and space invaders.
https://i.ytimg.com/vi/Wdyxh3_tTiM/maxresdefault.jpg
or literally break it so the stats go off the screen
https://steamuserimages-a.akamaihd.net/ugc/316748014355019968/95FA445A43F416726E0046C9E1CF526B8AC29719/
Yep. Fallout 4 is pretty much infinite leveling. I mean, the actual final level is 65,535 and only because the game will crash after reaching that level. Not because it is a hard coded level lock. Im sure a mod exists to fix this and make the game have a truly infinite level.
Any of those games I can break with enough time. Main character in Phantom Brave she moved 255 times before the first enemy got to act and she could pretty much kill anything that did finally Act when's 1 hit no matter what level of want dungeon we were doing for item leveling
In any game you will need to have progression caps. Computers are limited to specific numbers and infinity is only a theory in computer programming. "As of 2020, there is no such way to represent infinity as an integer in any programming language so far." You could add multiple values together to get a very huge number, but never endless. If you want endless there are games with 1000+ hours of entertainment, you just have to find the ones you like.
Second best is probably ARPGs like Diablo, Grim Dawn, the Adventures of Van Helsing, Titan Quest, etc. Even if you get to the "end" you'll be trapped in a cycle of endlessly creating new characters and making different builds with Microsoft Excel open next to you