More just having fun now, but I feel lossless compression implies deterministic decompression, i.e. there is one and only one signal which compresses to a given compressed signal.
Even if you had a signal which compressed to itself, it seems to me that there would likely be other possible signals which would compress to an identical compressed signal.
Good point, even if compressing and then decompressing does not change anything, you need to know that nothing changed, otherwise you lose information about the compression error.