It is possible, but he needs to continue his sessions and commit to the work. And you probably need to have some stronger boundaries with him if you're allowing these sort of situations to occur in your home.
What does "is possible" mean? That one person in the whole world did it?
No, the pwBPD are not going to change much for the better. It's about acceptance and coping. Everyone is free to make a choice - that includes putting up with a BPD partner. But the pwBPD is not going to become normal. Ever. This does not mean that you can't stay in a relationship with them or still love them. But don't expect that they will turn normal one day. Accept that they are who they are.