It is possible, I've seen people pull it off, but it is not for everyone. And people can tell you their own personal experiences and say hey you can do it too, but its not always true.
I'm actually a firm believer that when someone is important to you, it shouldn't change just because you broke up. And I worked very hard to try to maintain a friendship with my ex and was actually enjoying it as odd and awkward as it was at first,
but what made me finally just let go altogether yesterday was because 4 days ago my Ex's new bf went to visit his ex (the one he broke up with to be with my ex) and he didn't call my ex and ended up spending the night. My ex became very depressed and contacted me and told me all these issues he was having with his new guy, how his new guy couldn't keep him hard and he was only able to have sex with him by thinking about me and how he thought his new bf was sleeping with his ex, that his new bf was becomming distant and he was tired of it and missed me and if things didn't work out between the two of them if we could get back together.
I wrote him back concerned and told him maybe he shouldn't put all his eggs in his new bf's basket, and that if he was experiencing these things, maybe he should continue searching around before he was so set on o e person, especially on account of we haven't been broken up for even a month yet so he's kind of moving too fast.
He wrote me back really defensive, said his new bf wasn't cheating on him he was just scared of how much they cared for each other and it was really deep and he wrote out all of these comparisons between the two of us how his new bf's bad day is nothing compared to my bad day, how he can handle the distance after dealing with someone like me, and said he was just trying to make me feel better to boost my self esteem and he actually enjoys having sex with his new bf more than me and just a bunch of other really mean stuff.
Basically, I'm assuming he and his bf must have had a heart to heart and suddenly everything he said went out the window and he needed to desperately make things right by undoing the things that he'd said. Why he had to be so nasty about it? I have no idea and its something I wouldn't take from a bf, an ex, or a friend.
But what I'm getting at is, I would loved for us to have a healthy friendship, but that was a clear warning sign of things to come. Last thing I need is him and bf getting into an argument and he shows up at my new place trying to fuck me. I had to let it go. I learned a valuable lesson. Know when to let go. Don't compromise yourself for the sake of being kind.