I’m sure having an abusive boyfriend carried through to all other relationships. Once you’ve been mentally beaten down by someone, it’s difficult to build yourself back up, and comments about her appearance have been chipping away at Kate since basically the scene at the pool with the mean girls. I think there’s a chance he turns physically abusive, but the physical healing from abuse is easier (not easy, but easier) than the psychological healing.
And Kate has definitely gone on to have more bad relationships (though I don’t think that will be shown next week), when she was waitressing I think there was a reference to her being someone’s side girlfriend but I can’t remember exactly?
It could also be that he kills himself. A lot of abusers will threaten self-harm so that the person they’re abusing has to “prove” something like “Oh if I’m really that awful I’ll kill myself, will that FINALLY MAKE YOU HAPPY?” with the expectation that the other person is like “No I’m sorry, you’re right, I overreacted please don’t do that,” etc. Most don’t follow through with the threat, but I could see it going that way.
When present Kate found the photo, she and Rebecca discussed him almost nostalgically. There weren’t any “so glad he’s not MY problem anymore” type of comments that I would expect if he were still alive. I think he kills himself and Kate thinks it’s her fault and that just compounds her sadness, guilt, and shame from her father’s death.