> If that library is the system "libc" library or something similar, then it has to be reboot (not relogin). The only way that I can think for reboot-free updates, is to save the full state of the system, then silently restart everything to the previous state.

Restarting running services and logging in again is fully sufficient to handle a libc upgrade, at the very least on Debian. "Just restart" is maybe easier advice to give, but overshoots the target a little bit.