The usual answer is to issue them with a written warning - fix human issues with human solutions.
Meanwhile, I don't know if it works but try giving then a user short code that matches whatever system short code you have for routing external calls but which includes an A or an S element in the telephone number to allow sending the caller ID or to force the sending of a particular caller ID.
If you have Voicemail Pro I would be particularly cruel and see if routing all their calls via a callflow which blocks anything with a blank $CLI value works (never tried it, might not work internally).
Stuck in a never ending cycle of file copying.