All you need for this to occur is the window where both renames occurs overlap. A system polling to check if a, b, c, and d exist while the renames are happening might find all four of them.

I'm almost certain what the OP meant was if the commands were run synchronously (ie: from 2 different shells or as `mv a b &; mv c d`) yes there is a possibility that a and d exist (eg: On a busy system where neither of the 2 commands can be immediately scheduled and eventually the second one ends up being scheduled before the first)

Or to go a level deeper, if you have 2 occurrences of rename(2) from the stdlibc ...

rename('a', 'b'); rename('c', 'd');

...and the compiler decides on out of order execution or optimizing by scheduling on different cpus, you can get a and d existing at the same time.

The reason it won't happen in the example you posted is the shell ensures the atomicity (by not forking the second mv until the wait() on the first returns)

I don't think that's happening in practice, but 1) it may not be specified and 2) What you say could well be the persisted state after a machine crash or power loss. In particular if those files live in different directories.

You can remedy 2) by doing fsync() on the parent directory in between. I just asked ChatGPT which directory you need to fsync. It says it's both, the source and the target directory. Which "makes sense" and simplifies implementations, but it means the rename operation is atomic only at runtime, not if there's a crash in between. It think you might end up with 0 or 2 entries after a crash if you're unlucky.

If that's true, then for safety maybe one should never rename across directories, but instead do a coordinated link(source, target), fsync(target_dir), unlink(source), fsync(source_dir)