What is the most logical next event?

How to break up with someone who is threatening suicide
Emphasize that you care about the other person.
Tell your boyfriend or girlfriend that they are still important to you, even though you're breaking up. Let them know that you don't want them to hurt themselves.
Say something like, " i still really care about you, and i'm sorry this is so hard for you. " you might also say, " it hurts me to hear you say you'll hurt yourself.