Hi concerned - I hear you, I think this kind of pattern can be the most hurtful because it affects other relationships as well.
I would ask other members of the family as well as the BPD individual to please talk to you directly if anything is said that affects their relationship with you, and express willingness to hear directly from the source whatever the problem is. It may not solve but could disarm the situation, if you are clearly open to hearing everything directly, and asking to hear it directly, then hopefully those who value their relationship with you will honor that request and even push back when hearing this gossip, to redirect it to a direct conversation with you.
There are some tools on this site that talk about triangulation and the victim-helper-persecutor triangle - I think its called the Karpian drama triangle and how to transform that. Being aware of the pattern is the first step so good on you for identifying it!
I hope you have some stable people close to you who won't be affected and can help you cope with the situation.
One other advice, its good to model I think the same in the other direction - not talking negatively about the BPD individual with anyone that they are close to, and if you need to vent come here or talk to someone not in the situation.
At least that is my advice, your mileage may vary! Whatever works for you, and takes care of yourself.
