When is a threat of suicide real and when is it just a way to control people?

Every time a woman I know is asked to do something, she starts in with “I’m just no good, I’m a bad person, I should just end my life”.

She has cut herself a couple of times, just to prove it. She is under a doctor’s care for clinical depression and has been under 72 hour suicide watch twice this year for saying she wants to commit suicide.