During yum update, Python installation is updated. Do I need to restart running programs?

As the title says. If I run yum update(It's a CentOS box) and there happens to be a Python update. What happens if other users have running Python programs. Do I need to alert them to restart the programs? Or can they safely continue to run those programs basically indefinitely if they like?

To ask differently: Is the old Python version kept on the system(hard drive) for as long there is some process still open. Or does the update immediately overwrite the existing Python installation/binary? So existing processes continue to run only because Python interpreter is completely loaded in memory?

Yes.

Well, you don't need, as SvW correctly pointed out, but you should. Programs will continue running, but depending on how they're written, there is a theoretical possibility of them trying to load newer, and incompatible packages after the update.

Edit, To answer your "differently asked" question: Yes - open files may be deleted with POSIX, but this effectively just hides it from other processes, until it can be definitely deleted when the open handle gets released. Some C-API information available on SE.SO.

From a general point of view, updated programs can continue to run as long as you like, but of course fixes in the Python interpreter will not be available before you restart them. Check the change logs to see if this affects you.