Having a renaming script that evaluates to an empty filename Picard generates broken filenames in the form of e.g. "_mp3" (underscore followed by extension without dot).
The cause is that an empty filename will first result in a filename of just the extension (".mp3"), but leading dots are replaced by underscores (due to being invalid in Windows Explorer and being interpreted as hidden on Unix like systems). The result is "_mp3".
I propose Picard should keep the original filename in those cases.