Sorry for jumping in so late, also I have not yet read through all the posts so for give me if I say something that has already been addressed.
An off-hook is a short and many assisted living systems are set-up to alarm a nurse-station or dial 911 if the phone is off-hook and not dialed. Watch-mate is one type of software that will do this. As for this happening with the phone unplugged it could be a wiring issue or a pull cord in the the residents room since many pull cords operate off an analog port in the phone switch.