I dunno about the "work on why they were cheating", I'm not that way. You get my trust implicitly but once you burn that, it's ash.....to me, the talking should have occurred before the cheating, not after. I should think in a mature relationship if one is having doubts, they should be discussed beforehand.
Don't beat yourself up about exes who have lined someone else up before bailing on you, that happens to everyone at least a couple of times. Typically, those doing it are really good at hiding their true feelings and you're going along thinking everything is wonderful then they slam the door on your fingers......