Usually if they want to kill themselves, they won't annouce it
or you can be mean and tell her how will she look like if she kills
herself that way.
Anyway, I had an ex-classmate who is kinda like your gf. She uses
emotional blackmail on her bf lots and even goes to his place and
threatens to jump out of the window.
Ultimately, she didn't kill herself when he left her because I
guess there is only so much rubbish a guy can take though she was
like a wreck for the next month or so. Seriously, from a human
point of view, there will be a breaking point where you can go kill
herself if she wants because you don't care anymore. Ok, not
sounding humane now but I think that may happen.