Hi Girls3tsfire and a warm

It's so clear you're going through an immense amount of stress right now... it's like one domino fell, and now it's tipping over the rest of them. pwBPD do struggle deeply with loss and change, so while it's not surprising your BF isn't coping well with the loss of his great aunt, that doesn't make it easier for you -- because now you feel like you're losing him as he pulls away right now.
Tell me a little more about this:
My bf is also my caregiver, and his sister is also encouraging him to quit.
Can I ask (and you don't have to answer if you're not comfortable doing so), do you have a condition or diagnosis where you require medical support, and your BF is the one providing that?
Is this dynamic with his sister (where she tells him what to do) a new thing, or has it been going on for a while?
And do either you or your BF have a counselor or therapist right now?
...
It does sound like your BF is really struggling to process his grief appropriately, which makes sense given his BPD diagnosis.
Pulling away from you after experiencing loss isn't very functional or mature, but it's a known behavior.
How are you taking care of yourself, with the stress of him pulling away for the moment? Taking care of yourself is a really important first step towards improving your relationship.
Fill us in more, whenever you get the chance;
kells76