Diabetics, heart attack victims, strokes, asthma, hypertension, and so on are all chronic diseases that result in a level of functioning that is less than not having the illness. Disease imposes restrictions in both level of function and recovery. That said, she will likely never be totally well. As her therapist, you have to decide, with her input, where she wants to get to, and how to get her there. Since folks with BPD think differently than folks without BPD, you must frame the therapy in a way she can utilize it.
Borderlines are logical.
They wear coats in the winter, eat when hungry, like to drive nice cars, live in nice houses, do not urinate in their pants, and thousands of other things just like everyone else. In short, they learn to change things that make them uncomfortable in all other aspects of their lives. They understand that being naked outside in the winter is bad when it is 20 degrees, so they wear clothes. Your patient hates rejection, but is not learning from it. Therefore, as opposed to explaining the point as you understand it in your words, you have to present a very black and white descriptive method of change that she can understand as a borderline.