My friend had a terrible experience with someone like this.
They went out for a while and he was a nightmare, needy, controlling and possessive, she tried to chuck him a couple of times but each time he pulled the "I will kill myself" card. The final time she said that she was sorry but she didnt want to see him anymore and that was that.
Except he kept texting her for weeks saying he would do it, she just ignored him. Then he texted that he was going to take a load of pills, again, and it would be her fault he was dead, again, but that he wouldnt do it if she would take him back, again. She ignored him, again.
The next morning she had the police at her door because he had died.
Turns out he had taken some pills, texted his sister to tell her what he had done knowing she was due to go round that evening and left the door open so she could get in. Except she didnt get the message and didnt go round as a member of her family had been taken to A&E, she got it the next day when it was too late. At the inquest it was agreed that he had not mean to kill himself.
My friend has never really gotten over it, to this day she feels guilty that she didnt call an ambulance that night, or on one of the other times he threatened it because that might have brought him to his senses :(