You fclose the handle when you're done, or you create some kind of synchronized semaphore, if you wanna be extra.

The issue is really around having multiple handles for writing (not just reading or appending), and the number of times you actually have this problem here is vanishingly rare.

I'm not saying it's a good idea to open it more than once at the same time, but nothing is preventing me from doing it, so I'm not sure what is meant by, "a file is a singleton"?

In most cases nothing, the OS or applications will naively read it or write what they believe the current state to be.

They need to use some form if mutual exclusion? Same as for non-singleton objects in a process.