she would show up and see what I was up to occasionally without interacting with me directly (at the same social events, etc) before she finally disappeared from my life forever, but it was obvious she wanted me to chase after her so she could ruthlessly discard me again and fortunately I didn’t take the bait.
Know exactly what you mean. My ex would break up with me then start coming back into the pub where we used to go. She wouldn't speak but she was letting me know she was still there and l would end up chasing her, ignoring the red flags.
Probably knowing I'd chase her only made her worse and she'd break up again and again. No idea what she was doing when not seeing me - she might have been seeing others then only coming back to me when the new thing fizzled out. With BPD's it's always a case of 'out of sight out of mind' and it's like you never existed.
She eventually threw such a horrific tantrum where she was so detached from reality that I realised I didn't know her..and didn't want to know her any more, so when she broke up with me I didn't chase. I heard later that she'd come into the pub looking for me but this time I wasn't there. If she'd been genuine about getting back together she could have contacted me in any number of ways so it was obvious she wasn't really bothered.
You'll never get any closure with a partner who can't appreciate your feelings and can discard you in a second - in their mind they've never done anything wrong.