Firefall, it is very kind of you to let her stay there and try to help her, but maybe draw the line at how willing she is to help herself.
She is probably qualified for disability income, is she willing to talk to them about that? And willing to pay something for staying with you?
Is she willing to find counseling to help her with her BPD and addiction issues?
There is help out there for her, you don't have to carry the load alone. Because of how she is, perhaps take the initiative and find the resources and then discuss them with her. She doesn't sound like she is capable of doing that for herself, so helping her a little on this might lead her to a better life.
My prayers go out for both of you, it is very hard to watch anyone we love suffer.
Hugs