Warlord

[Tyberius]

The only weird thing is that the possessed Kes breaks up with Neelix so, presumably, he won't hang around her and potentially realise what's going on, but it sticks! They stay broken up.

Maybe Kes wanted to break up with him anyway. Or maybe she was still in control of herself when they broke up. Was it possibly a cut scene that was taken out?

I gathered, from other dialogue that Kes felt guilt for allowing the dude to control her, that she felt that maybe it was her that broke up with Neelix. Also, she was violated very deeply and probably didn't want to be close to anyone for a long while.