Some MUDs used a very cool trick to avoid this, called “copyover” or “hotboot”. It’s an idiom that lets a stateful server replace itself while retaining its PID and open connections. It seemed like magic back then: you recompiled the server, sent the right command, everything froze for a few seconds, and (if you were lucky) it came back to life running the latest code.

Xpra is known as "screen for X" : its seamless mode allows you to run X11 programs, usually on a remote host, direct their display to your local machine, and then to disconnect from these programs and reconnect from the same or another machine(s), without losing any state. Effectively giving you remote access to individual graphical applications. It can also be used to access existing desktop sessions and start remote desktop sessions.

(I knew about Xpra in 2021, but forgot about it.)