I do believe it's BPD. I think I have some slight version of it myself, and it's a LOT to take in. Sometimes I get so attached to people that it really feels like I'm going to lose myself the moment they leave me, so I try to hold on to them no matter what, even if it ends up hurting me more in the end. It's a really hard process to learn to let go of people when they no longer want to be a part of my life, and this is coming from someone who only has a mild version of it -- I don't physically hurt myself when this happens, but it's still a huge low point of my life and really suffocating.
Yi Soo definitely shows the signs of BPD and definitely deals with it in the way someone with BPD would. She gets irrationally angry and manipulating when she realizes she might be left; she makes it worse for everyone and even if SHE'S suffering too, at least Kang Woo Il wouldn't leave her and she'd still have something to hold on to. When she can't get him back, she resorts to harming herself -- because Yi Soo without Kang Woo Il feels like she can't exist.
I realize that you've posted this when things weren't yet cleared up, but you couldn't have been more RIGHT about this whole situation. Yi Soo needs to deal with her problem, and that's the best thing that can happen for everyone involved.
Of course they made the whole family wacky; Hwan Gi has social anxiety, Yi Soo with her BPD, the father has anger issues, and the mother shows signs of histrionic personality disorder. But I think it added spice to the story. I'm going off topic here, but I hope they'll handle Yi Soo's problem the same way Hwan Gi did: therapy, counseling, and overcoming it alone, not being pushed to be someone who she isn't.