But that doesn't cover all the bases, because it is perfectly possible for a file handle to get closed without the program doing it explicitly.
Are you sure about this? Well, I've never programmed under Windows, but under Linux I haven't seen yet any single case when the file descriptor would be closed by the kernel. The rule is simple, if the user opens a file descriptor, the user has to close it. There could be libraries that close it for you, but those libraries are running in the application space.
So, if you make sure, that you remove file descriptor from "select" before you close it, then things work fine.
As to example, I've never used IO::Select module, but many years ago I've created more or less simple module that uses "select" directly. This module still works for many of my application, even though I consider it to be very poor. You can get it at http://vandal.sdf-eu.org/NetHandling.pm if you want.
I guess the main reason why one can't find good examples of using "select" is just the fact, that it is not that simple. To make things really working, one has to take into account many details. As result the code becomes hard to understand. Actually, if one tries to implement the same stuff using threads, then at the end the code would become equally complex and hard to understand. So I don't believe one would be able to provide simple but yet robust example of using select or threads for networking.