Well, to be honest, I'm currently going through that with two men and a woman simultaneously, and until rather recently it was actually four parties. And in all four cases, to the best of my knowledge, both parties care.
Why don't we talk to each other?
1. Mutually abusive relationship that I got PTSD from (somewhat worse on my side, I guess, if only because I ended up quite mentally ill by the end, so I had to deal with that, too). I went back to talk to the guy after I stopped having panic attacks every time I thought about him. We now have a fairly cordial relationship, I think.
2. The dude asked me to go on a date electronically; I said no, I really didn't have the time for whatever our relationship was; he got upset because I "broke up with him over Facebook" (this is what happens when you mostly contact me through Facebook and try to manipulate me into doing stuff I don't want to do on my birthday). He's still pretending I don't exist, but I send him happy birthday messages and whatever, so relations are cold but not really horrid.
3. I broke up with a guy in person after an 8-month relationship. He had told me many times that he was disinterested in me as a partner and that he wanted to break up with me after I graduated. He also told me that he hoped I found someone, and did basically nothing to try to keep me with him or ingratiate me to him, so that's why I finally called it quits--one person was in the relationship, the other person wasn't, it was splitting up time. Taking all of this in consideration I asked out a mutual friend a few weeks after breaking up. He now hates me and looks at me with revulsion if I say hi, because apparently I must have been "interested in that guy the whole time and never cared at all." Suuuuuure.
4. My best friend/someone who used to be in love with me (and with whom I was in love, though I couldn't admit it to myself) doesn't talk to me anymore. I have no idea why, but I think that if hard pressed then she wouldn't say she doesn't care about me; maybe just that she doesn't like me very much.
Anyway, to the best of my knowledge this happens when there's an injured party and either they're not capable of talking (a) or they decide that they want to punish you for past transgressions (b, c, and d) more than they care about your well-being.