Welcome Yesiam: I'm sorry about the situation with your sister. Stress and change can prompt a person with BPD (pwBPD) to have a melt down. It's not your parent's fault for moving. It was just a matter of time until there was some event, stressful situation or loss of a friendship, etc. that caused the first episode. You are right to anticipate that whenever your parents have significant health issues and/or pass, it will more than likely cause emotional dysregulation with her.
Reading about
FOG - (DEALING WITH FEAR, OBLIGATION AND GUILT), can be helpful for you to read and to share with your parents.
I could be helpful to read this article:
GETTING A BORDERLINE INTO THERAPY. It generally doesn't do any good to force someone to participate in therapy. Sometimes, you might be able to prompt someone to go to therapy, but unless they want to participate, there is generally little or no benefit.
SETTING BOUNDARIES will be helpful for you. Boundaries are for your benefit and protection. They are up to you to consistently enforce them. You might set some boundaries for your benefit and your parents may have their own.
You can't change your sister. The only thing you can do is learn various communication skills that will make things easier for you and should tame some of your sister's responses.
Is your sister self supporting? Does she live alone or with your parents?
I don't want to throw too many links at you. After you click on the green words above and check out some of the links, you might want to browse through some of the links within the large green band at the very top of this page. There is a "Tools" menu there. The lessons on ":)on't Invalidate" can be a valuable one to learn.
Some people like to read lessons and then come back to their thread and post to check their understanding and to practice applying some strategy. After reading about boundaries, what are some possible boundaries you might want to put into place?