I have BPD and my partner has to deal with me and it can be very difficult for him. I feel like I've driven him up so many walls, but he still insists on sticking with me, which I am so extremely grateful for. If you are looking for a long-term relationship, it is very important you take care of yourself and incorporate some healthy boundaries between you two.
I am no expert though, so I think it is important to seek professional advice on how to take care of yourself and the relationship, and how you can help your partner - seeing a counselor/psychologist, calling a helpline, etc. could be some ways to ask for advice or have a chat about how you are feeling.
Does he/she have a psychologist/has tried DBT therapy? For me, those are some of the better options out there. Do let them know they can get better and that there is help out there for them, and for you too. A relationship with someone with BPD can be difficult, but not always. Sometimes it can be very rewarding.