Fantastic film, so what did you think happened to Hae-mi (spoilers)
I personally think she is the character of Yuen-Joo, the "new" girlfriend of Ben's who we meet when Hae-mi leaves the scene. Hae-mi did mention herself that she had plastic surgery done before and probably that's why the cat is in Ben's apartment. It's clear to me that Hae-mi wanted rid of her old life as she seemed to have run up debt and hadn't a friend in the world beside's Jong-su and wanted to start her life over again. The way Yuen-Joo act at the last party reminds me of how Hae-mi reacted during the earlier party with Ben's friends. Also the bracelets left in Ben's bathroom also say's she's living there.
I thought for a while Hae-mi and Ben were using Jong-su to get revenge on him for calling Hae-mi "ugly" as a kid, some people hold grudges you know for that long. But even was that true, as Hae-mi is known to lie. I didn't think Hae-mi wanted Jong-su around look at how disinterested see looks when she's with him, probably Ben pushed her into it as he seemed interested in him, Making the ending somewhat tragic. As Ben seemed bored with his life and seemed interested when Jong-su was around.That's my take probably wrong lol