When you open a file in Linux, you hold on to the reference of the underlying inode, which means if you load myLib 1.0, then update to myLib 1.0.1 using apt, then all the previously open programs will be stuck on the old version. This is a security issue at best, since unless you restart, there's no way of making sure nobody uses the old lib anymore, but more frequently a source of crashes and bugs, since myLib 1.0 and 1.0.1 might not be perfectly compatible. If I update Ubuntu, Chromium is almost 100% guaranteed to crash, (since the newly started processes use different lib versions), but I've seen other crashes as well.

In summary, I can't recommend you continue using your Linux machine after an update without a restart, since you are open to an entire category of weird bugs.