I would like to explore those who threaten suicide from another angle.
Someone says, "Give me your money or I will beat you up. Break your arm or your leg."
We consider this person a criminal. Seldom do people stop and think they may be a person with a specific personality disorder that may need help.
Someone else says, "If you don't give me an escape vehicle I will shoot this hostage."
We react pretty much the same as above. No one wants to baby this person, everyone wants to send for the swat team.
But then someone says, "If you don't marry me I will commit suicide."
But now we say the person is in need of help and love and whatever -- Yet the threat is just as devastating as either of the first two -- And far more subtle and vicious -- because now the person at risk of violence is themself and you are at fault for having caused it.
While I personally can understand the concept that the person who threatens to break your leg, or hurt someone else to get their way, needs mental and emotional help -- I think the correct immediate response is to treat them as a criminal. To react as though under a criminal attack.
And while I can appreciate the concept that a person who threatens suicide may indeed need mental and emotional help -- I do not believe the person being threatened can be faulted for reacting as though they are under a criminal attack.
Because the threat is just as vicious as if they pointed a gun to your head or to the head of your spouse.