its a mental problem and a tool in their arsenal.
99% of the time it's just a way to manipulate because they know that it's a good way to make most insecure/inexperienced men cave to their emotional demands.
I'll admit I dated some really mental girls in my late teens and early 20s, like really disgustingly mental girls who would overdose, cut themselves, and yes, threaten suicide - often. I was a beta retard at the time, didn't know any better, hadn't dated any girls before, and I fell for it every time. It made me cry when a girl would threaten suicide and act all sad. I kept falling for it for a few years in two separate toxic relationships.
Finally I just became worn out and sick of it and started telling them to go ahead and off themselves if they threatened. The last time she took a bottle of pills saying she was killing herself I just called an ambulance for her, got in my car and drove away, never saw or spoke to her again.
That was years ago. Now if I meet a girl or start a relationship and find out she has mental problems (alcohol abuse, claims she was raped/abused, drug abuse, cuts herself or has old scars indicating she used to cut herself, claims she used to be a slut, or threatens suicide) its an instant NOPE for me, I end it right away on the spot instantly.
Life's too short to spend with fucked up mental women and anyone of them who has a history of these kinds of issues is likely still going to have some lingering problems even if she claims "shes changed."
Advice to you if you're with such a girl threatening suicide and trying to manipulate your emotions: get out of the relationship ASAP. She'll cry, she'll grab onto you, she'll plead and beg and promise to change, and when you stand firm and say NOPE she'll threaten suicide as her last ditch effort to change your mind, but you have to be strong and just say "do it faggot" and leave and if she actually does it, well that sucks but its not your fault or problem.