Most Helpful Guy
GTFO, that is not a place you want to be. Offer to help them find treatment and make it clear that you do not want to be in a relationship with someone who will threaten to hurt themselves over someone leaving. That is not love anymore if they are resorting to emotional manipulation.
Most Helpful Girl
That's emotional manipulation and if it's a repeat pattern then that's emotional abuse. If you're in an abusive relationship with someone like this then the best thing for you to do is leave. If they threaten to kill/hurt themselves then you call the cops and have them do a well being check on them. Most likely they are just doing this to control you though and will be pissed that you called them out on their bluff and abuse.