Even if you are a burden and some part of them will be relieved when you're gone, I believe that another part of them can see past your disorder and see the 'real' you, trapped by all these problems.
I've met several people with BPD during my long stays in psych hospitals, and I think I could be good friends with them, despite these obstacles. Especially when they're aware of them, like you are.
I mainly reply because just recently I've read that TMS can help with BPD (magnetic brain stimulation, very safe and basically no side effects compared to drugs). And not just with comorbid depression, but also with impulsivity, mood changes etc. There are ongoing studies about this.
E.g. see here:
http://pbsciences.org/en/ArticlesDetail.aspx?ID=460 or
https://www.ncbi.nlm.nih.gov/pubmed/30633728, both from 2019
I will try TMS as a last chance to fix my extreme fatigue, hoping that maybe my depression is still the cause. The good thing is, after the 4 weeks of treatment, it either worked or it didn't. I don't have to endure 10 weeks of drug side effects just to realize it doesn't change anything..