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Her ex-ex boyfriend told her the other day to just kill herself and unburden the rest of us. I get his hostility. We've broken up but she still talks to me, about how hurt she is, about how suicidal she is. I've done my damndest to assure her that she isn't worthless, that suicide is not the answer, but I'm also tired of hearing about it every day. I've been in pain before, severe pain, I didn't tell everyone I was going to kill myself over and over.

I get why her other ex said that. I think it's hit, but I get it. He's tired of being told how much she wants to die. He also told her the reason people leave her is they don't want to care. I agree with that too. There's too much to care about all the time. She thinks I'm a robot, but there's just no room for me to have a damn feeling. She uses up all the feeling space and if I do show a feeling she attacks it. So yes, being with her is endlessly unsatisfying and painful but I can't say that because she's already threatened to kill herself over and over and I believe her. She has no job, she has no family, and the people she lives with have made it clear they are sick of her hit. So she's perfectly situated for complete despair. I can't get her to go to therapy and frankly she can't really afford it. She uses up all my time either because I'm worried about her, or she's asking me to spend time online iwth her in games and on skype and I know if I say no, she'll want to know why, and if I say no to that question she'll break down crying and call herself worthless and start moaning about killing herself. When the statistics are 1 in 10 kill themselves, the threat is too real to treat lightly.

I just can't penetrate, I can't push her to do anything constructive. All she does is leach and whine and cry and threaten and I want out, but I am terrified that my leaving will be the last straw that leads to death and I cannot live with that. She found a sucker... .

That's quite a dilemma you're burdened with. The time to detach from a suicidal pwBPD is immediately after you do the best thing you could possibly do to help - call the police and an ambulance.  They will know what to do from there. You might think about letting her hit her own rock bottom so that she can get the help she needs.

Agreed 100% with aussieozbourne.  The reason you can't cope with her is because you literally can't-you aren't a professional and you can't really help her despite your best intentions.  You are not her keeper; you are not obligated to spend the rest of your life trying to keep her alive. 

Personally I think(after bitter experience) that if someone is suicidal the cops should be called immediately.