My first bf did this a lot. He was 10 years older then me and I was only 15 when we started dating so pretty immature. At first I was utterly convinced he would until a friend pointed out it followed a very predictable pattern. Every time I clawed back a little self respect or control, made a friend, wanted to go out with friends or family without him he suddenly couldn't let me leave because he was scared he'd end his life.
The last straw was when I wanted to go for an interview for a job he had forbidden me to apply for. because it would hand me my freedom
He picked up the knife and threatened to slit his wrists and I calmly told him to do it in the kitchen so I didn't lose the deposit if he ruined the carpet....
I did feel awful about it as it was mean but he hadn't done it the other 50 times he'd threatened so the odds were good.
I did get the job and with it my freedom (it was live in childcare for a pub landlady, I think he knew that he'd never be able to get through the barstaff to the accommodation upstairs)
He is still alive I think.
Sadly my charming mother has decided to use suicide as a threat against us now so I'm gearing up for all this shit again. My new plan is to disengage as soon as the threat comes and call an ambulance so she can explain to them she was being dramatic..... (feel bad about wasting the ambulance though!)