Last Friends - A bit obvious one. This revolves around the domestic violence case. She keeps going back to him and her friends are trying to intervene.
Cheap Love - This one starts off badly (to put it mildly) but for some reason she sticks with him and they spiral downwards together...
Kimi wa Petto - Keeping a man as a pet... Well, it's weird one, for sure. Unhealthiness and whether or not it's romanticised is up for debate.
She is Wow! - Maybe this one for marriage gone wrong. Husband brings home his lover and declares he'll live with them. It's an odd drama.
Valid Love - I think this one fits the bill somewhat, if we consider affairs unhealthy... She has an affair and they have to work out all the relationship problems this causes (and was caused by).
Then there are a few taboo student-teacher ones i.e. Romance, Loveholic, Biscuit Teacher and Star Candy, Big. Romance is probably the least romanticised one out of the bunch.
Sorry I Love You also comes to mind but it's been too long since I saw this and can't really remember how it handled the relationship...