Hello Warshire, welcome to the group

As your DD is 45, I imagine you've been through a lot over the years.
A couple of positive things stand out to me -- one, she has an official diagnosis of BPD, and two, she's still in contact with you (even though it's mostly about money).
Is she accepting of her diagnosis? Does she seem to want to be in treatment?
Of course, there's always so much nuance and so much to talk about, but I wanted to briefly address a couple of your questions:
I don’t know how to get her out of this relationship so her mental health will improve
One of the most challenging aspects of having a child with BPD (from what I've heard; the pwBPD in my life is my husband's kids' mom) is readjusting our sense of who is responsible for what, and what "help" looks like.
People with MH issues often have to hit rock bottom in order to personally choose to make changes in their lives. We would love for rock bottom to be less extreme, yet often it is pretty intense. If we try to rescue them from their choices (toxic relationship etc), they don't have an investment in the change and it doesn't stick. It may be excruciating to watch and wait as she struggles through what she's chosen, yet she is an adult, and trying to save her from this relationship unfortunately probably won't help. She needs to go through the process on her own.
is it wrong not to support her financially? I don’t want to make our relationship worse.
In short -- she's an adult child, so no, it's not wrong to not support her financially. Paradoxically, she may have more respect for you, and your relationship may move to a more stable place, when you choose to have firmer boundaries about how you two interact. Giving decision making back to the pwBPD, however challenging for us, is long term better for the relationship. A brief example of how that might look could be: "Honey, that sounds really difficult to be that low on money. Even though I don't have any to provide, I'm confident in your ability to find a solution. Where do your friends turn when they are on a tight budget?" Of course, that's just an example.
One more question as we keep talking -- does she have any kids? I know when there are grandkids in the mix, it's exceptionally hard to watch.
Keep posting whenever works for you;
kells76