Criminal negligence maybe, if the woman was in a position to understand that the girl was in danger of that action. Considering many psychologists will attest to patients walking out of their office just fine and then going to kill themselves, it'd be hard to prove she could make that assessment. I suppose if the girl stated an intent to commit suicide and laid out a plan, then negliegence might be applicable. That would be a hard case to prove though.
I can see harrassment working the best and is probably the most justifiable course of action. Followed by a civil suit, which would probably be won.
There is no law against being a pathetic human being though. Also if the girl felt that was her only way out, then something else in her home was certainly playing on her.