Has she made attempts before? I found the below in "Stop Walking on Eggshells" by Paul T. Mason & Randi Kreger:
WHAT NOT TO DO:
...Avoid the following actions with someone threatening suicide:
*Don't get into an argument with the BP (Borderline Personality) about whether or not they are serious about wanting to die--even if you're angry and feel like venting. The person may attempt suicide simiply to prove you wrong.
*Don't confront the BP and accuse them of manipulating you. Again, this may turn into a power struggle. If the BP is asking you to do something that is against your better judgment, follow your instancts. However, if the two of you are in a session with a mental health professional, it can be helpful to talk about how this behavior is making you feel.
*Be extremely cautious about relenting just to prove that you really care. Contrary to what an angry, distraught BP may be telling you, you don't have to prove anything. "When you give in to the threats, you will still be angry, the BP will still be at risk for self-harm at any time, and the underlying issues will not have been addressed. Plus, it is likely that the same scenario will repeat itself again."
If you have a history of complying with demands because you believed that suicide was imminent, we suggest obtaining professal help for one or both of you before the next crisis occurs.
WHAT TO DO
Suicide threats that feel manipulative are the ultimate in no-win situations. Whether you copmly with the BP's wishes or not, the risks are unacceptable. SSo, Newman and Ellis say, the best thing to do is to simply refuse to be put in this position, despite the BP's attempts to make you feel responsible for their life and death. Just say no, following the guidelines that follow.
Express your support and concern for the BP while firmly maintaining your personal limits. You can do both, even if the BP thinks otherwise. You can accomplish this with mirroring responses that put the choide of life or death back where it begins--with the BP--while stating as strongly as possible that you care about the BP and you want them to choose life and seek help. Newman and Ellis give these simple responses, which we have paraphrased:
In response to "I'll kill myself if you leave me"
I'm not breaking up with you to be cruel. I'm very, very sorry that this hurts you. I want what's best for you in the future, but I just can't be part of it. And even if I were to stay with you, that wouldn't solve our problems. For one thing, your life's worth should be based on much more than just being in a relationship with me. Secondly, I know that you know deep inside that our relationship shouldn't be based on me staying because I'm afraid of you dying and you staying because you think you can't live without me. That's not healthy. I care about you. And because I care about you, I want you to live. And I want you to find your own happiness and your own life's worth, without me."
BTW Borderlines have a lot of the characteristics of other psychological profiles, so I felt this info might be helpful. Sorry you are going through this. Don't take offense, but it might be worth your while to talk to a professional to figure out how you got caught up in this relationship so you avoid in the future.
~2Shy (has a Borderline mom)