Welcome OzK: You sound like a very compassionate person. Are/were you a foster mom in a legal sense, or has it been an informal situation?
My beautiful daughter is damaged by the trauma of once loving someone with the unpredictability of BPD. She now has her own anxiety issues. She both admires and hates me for standing by this kid and resents any time and especially money I spend on his well-being. My home is often a battlefield.
My BPD boy is a delight, a mystery, a constant worry. I am slowly learning to put aside judgement when he makes unwise choices; as his 'safe' person his reaction to my disappointment can be devastating. . .
I hate that he can't live with me and I'm exhausted by the constant worry about his mental health when he's on his own.
Other than your compassion, is there something that draws you to your "BPD boy"? Is it possible that you are paying more attention to him, as opposed to your daughter?  :)o you understand that although your daughter might think it's great that you are helping her ex partner, he is an ex for her. I'm thinking that has to be hard for her (or at least very uncomfortable). Can you try and reverse the situation? What if you broke up with a partner and your daughter took it upon herself to rescue him? Might you understand how awkward that might be?
I'm not trying to criticize you. Just trying to help you see your daughter's perspective, when you say she sometimes hates you. Might the damage to your daughter keep on ticking, because you are so involved with her ex? When people break up with someone, they generally want/need to get them out of their life.
I got him to see a psychologist as he sobbed and begged me to help him find out why his thinking was so 'different'. We helped him get an allowance from the government, got him back into school and worked with a charity to find accommodation. A psychiatrist for meds and a new psychologist
He's learning to recognise the warning signs of a crash and will let me know although learning to self soothe is a long way down the track. . .I'm so angry that the facilities to help him are largely in the private sector - something neither he nor I can afford
But you know what? Unlike a lot of people's experiences on this site he is not malicious or manipulative and he doesn't steal or lie. On a good day there is a flicker of ambition and the hope of a future. With lots of professional help and a whole heap of patience I think he might get to a good place. If only love was enough!
I'm thinking your foster son is idealizing you right now. How does he currently act towards your daughter? Is your daughter drawn into a
DRAMA TRIANGLE with you and her ex?