Hi Issy,
DBT while it was conceived to treat BPD is an effective form of CBT for a larger spectrum of emotional and behavioral conditions. So if there is an awareness of the fact that things are not optimal, the person not feeling well and possibly envious of others doing better and a desire to change then I could imagine it being possible and effective to steer a friend toward DBT. Overcoming anxiety, better self management and being more effective with others are all positive goals fitting well with typical weaknesses of a pwBPD. Less analytic (not bothering much with the question why are you kaput) and more practical oriented should also be good selling points.
I see the only way is by building trust, which I want to work on now, I am still practicing my validation skills. I have read the article Anosognosia and Getting a "Borderline" into Therapy on BPD Family, it says as second step: reinforce the developing awareness. Any examples?
There are some stories where members have taken a stand as they saw no way to stay without partner going to therapy. This can work or this can lead to break-up.
Then there are stories where partners decided after a while to listen and go to therapy - this plays out over months and years and pin-pointing exactly when it happens is harder. They sometimes take the form of the ultimatum story but when looking closer it is much more a developing awareness and then a shove story. With this in mind you should find quite a number of them.
There are also stories where the situation improved somewhat and no therapy was involved but these are less interesting here as your friends problem is not with a specific partner who learns skills.