I had a friend like this when I was in high school/college. It was always about how horrible her life was and how miserable she was. Truthfully, I never really could see why her life was horrible. She had parents and siblings who loved her, a nice house to live in, plenty of food, nice clothes, etc. She just liked being dramatic and being the center of attention.
When we went off to college she lived down the hall from me in the dorm. The drama continued. She would complain about having to stay up all night taking care of her drunk, sick roommates and again about how miserable her life was. She would not listen to advice and just preferred to wallow in her misery. About my junior year she started playing the suicide card. It took me over a year to figure it out, but finally I realized she would toss out suicide when people stopped focusing on her. We had all been trained to "take suicidal threats seriously" and so we would drop everything and go pander to her. It made huge chunks of my college life hellish and miserable. I was in a very demanding major and was stressed all the time. There was never any sympathy or support in my direction. It was always in hers.
The summer after graduation I finally cut her off. I had recently been diagnosed with a very serious chronic illness and I felt absolutely miserable. She came to visit and instead of asking how I was and how she could help, the entire visit was about how horrid her life was. At that point I realized that she had never been a true friend. I said goodbye and walked away. I wish I had done it years earlier.
A true friendship is give and take. A true friendship means you truly listen to each other and help each other out. If you are the only one giving and you are the only one listening, then it isn't friendship. It's being used.
I can't tell you what to do with this friend, but people like that can suck the life right out of you. Sometimes, you have to just walk away. They aren't worth it and will never change. Next time she threatens suicide, call her parents or a teacher and report her. It is not your job to carry her emotionally. It is the job of the adults around you. Next time she complains tell her that you are sorry she is unhappy, but that you would like to talk about something else. Then change the subject. She will either get the point or she'll continue to be a drain and you will know what to do.