Now, that's a tough one, LOL. I honestly believe that it depends on both sides involved. For me, staying in touch with an ex was never an option, but it's only because of the way things ended. On the other hand, if it was a relationship that started as a friendship - I guess there might be a way for the two to stay in touch..
Here in Israel we have Yom Kippur soon, so we must forgive and forget everyone, so... Have a Shana Tova ! [Happy new year..]