Once I trully consider someone family and make that bond I care about them for life.
A family member and one of my best friends from an earlier point in life died and I missed her I just wanted to touch base with her.
This is all certainly understandable. Attachment bonds form in all sorts of relationships. The emptiness and sense of loss when a relationship ends is common, the stages of grief experienced etc.
If you don't mind sharing, who were the family member and the best friend? Also what do you think your former SO would have been able to provide while you are experiencing dealing with these losses? Are you feeling that your former SO would have been supportive, or are you struggling with the compounded loss of all three, the SO, family member, and the friend?
There is nothing wrong with reaching out but when one deals with a pwBPD, you have to accept that they are uncapable of geniune care and support, even if they are somewhat emotionally invested, difficult life situations are most likely triggering a regressive breakdown, as mine started sexually acting-out when I was grieving the loss of my grandmother, or met with painful indifference, even lashing out.
My heart goes out for Blim. It's hard to accept that someone you cared about deeply can't provide any comfort in a difficult life situation, but unrealistic expectations will only prolong the pain.