I do not think you should.. You can not fix her problems. You can be her friend and support but she needs to fix herself.
So relationship wise, is not a good idea right now. It is just going to cause future and bigger headaches.
She needs to learn how to get help, professionally and stop cutting, which is NOT NORMAL. There are series series issues here.
Next time she runs away, or if this was the last time. That is it. Let her be and do not even bother.
You can not force somebody to stay with you. That is abuse as well. She will come to you if she needs any kind of friendly advice or support.
Joe