Does Isabelle know about Cys past relationships with his high school students? Or the women he raped in college? If so, how does she feel about that?
Cy being a college student was so long ago by the time Isabelle shows up that she never finds out what he did back then, especially because it wasn't really known.
However, about two years into their relationship she hears through a "friend of a friend of a friend" situation that Cy used to screw his students back when he taught at Trinity, and she does ask him about it. He tells her the truth, which Isabelle more or less confirms by talking to Lynn about it, and Lynn's openly critical way of discussing it helps reassure Isabelle that Cy isn't downplaying.
After a period of freaking out about it, Isabelle comes to the conclusion that because Cy wasn't violent with his students and because he doesn't do it anymore it isn't worth ending the relationship over—an example of Isabelle's very pragmatic, somewhat dingy sense of morality. She thinks the good Cy does her is more important than the moral gesture she would be making by dropping him, especially since the latter would be kind of hollow. Her lingering concerns fade with time.