If you use an editor with safe saves this might not even happen because that works by saving to a temp file and doing an atomic swap, and unlinking the old file. In that case, I believe the script should continue as written, because the fd should point to the unlinked file. I believe vim does this by default, for example.

But I've never seen a person editing a bash script without an editor that swaps in a new version of the file until today, so never knowingly encountered this bug before.

It should be fixed.