How has the family berm demonstrating sympathy/empathy?
A Dx, while on the surface may seem good, can sometimes result in more severe behaviors. Cancer, for example, is what you have. Bi-polar might be taken in a similar manner ("I have a chemical imbalance" whereas, diagnosis of a personality disorder can be taken as "there's something wrong with me as a person," i.e., identity.
If he's been recommended to a residential treatment center, is there also a dual-diagnosis of substance abuse?
Naughty Nibbler pointed you towards lessons here, which contain communication techniques developed by leading experts in the disorder.
One of the core emotions of a pwBPD (person with BPD) is shame ("I'm a bad person, and unloveable". Trying to validate while not hitting that target is hard, to be sure., but we can help
If your brother has narcissistic traits as well, this might help. Tell me what you think:
Dealing with narcissists by reinforcing the positiveTurkish