They don't, the program keeps using the old library until it's restarted. Some Linux distributions restart daemons when they or their dependent libraries are updated, but that can't be done for desktop software. Firefox sometimes notices it's been updated and pops up a warning with a "Restart Firefox" button (which keeps the session state), though AFAIK it's only for updates to Firefox itself, not for any of the libraries it might have loaded.
If you never restart a Linux desktop (or at least log out), you will be running outdated libraries, even if you run updates in the background.
(The best solution would be what Android does, where every program is supposed to know how to checkpoint itself, and they are forcefully restarted on a upgrade, transparently to the user. But even there, updates to system libraries still require a full reboot.)
If you never restart a Linux desktop (or at least log out), you will be running outdated libraries, even if you run updates in the background.
(The best solution would be what Android does, where every program is supposed to know how to checkpoint itself, and they are forcefully restarted on a upgrade, transparently to the user. But even there, updates to system libraries still require a full reboot.)