Quake 1’s multiplayer is powered by fans of the game using a custom program to host their own multiplayer servers. The “original” multiplayer servers have been shut down for years. You can no longer play on “official” servers, only fan-created ones, which requires you to download 3rd-party unofficial software.

Battlefront II (Classic) is the same. The official servers are gone, but fans have created custom servers that players can connect to using special, non-“official” custom software.

Most Call of Duty games still have multiplayer communities because Call of Duty multiplayer servers use peer-to-peer connections. The game chooses a “host” player, and all the other players in the lobby route to that player. However, the larger online communities for older Call of Duty games use 3rd party software to create their own dedicated servers and have fans connect to those instead, rather than relying on the inbuilt peer-to-peer system.

Old Valve games like Team Fortress Classic, Counter Strike, and Half-Life never had official servers. They all used community-built hosted servers. That was one of the appeals of using Steam - they gave you the software needed to host your own server, and the framework to make that server easily visible in the Steam servers browser.

Online games stop working when their company-hosted servers go down. Online games can continue to work, potentially forever, if their multiplayer works through dedicated servers instead. It’s all about how the developers designed and coded the multiplayer component.

Some online games, such as long-term MMOs, will pretty much only work on a company-hosted server. As a design choice you do not want players to have access to their character files, you want all player-specific everything on the server.

So yeah, some online games will stop working. That’s just the way of life.