We RARELY have much control over the way things end - especially if we are not the ones wanting things to end. "closure" means literally just that - CLOSING - ending, stopping, no longer open, done, over.
Having closure means you no longer FEEL within a relationship - you know it is over, and you are done with it. It does not have to mean you no longer CARE about someone, it means you no longer have any emotional attachment to them - very different feelings. For example - when I found my boyfriend had lied to me, I broke it off with him, and almost instantly lost all emotional attachment to him. I CLOSED that emotional door behind me and moved on. HE however, did not want to emotionally break it off and tried for months to win me back. Because I no longer FELT any strong emotion for him even though I still LIKED him, his efforts were a waste of his time. Now, years later, we are still good friends, but no matter what, I will never FEEL the way I once did for him.
Some people just cannot bring themselves to getting people out of their emotion bonds - they hang on, want to talk it out, figure out every detail or why this or that happened, and so on and so on..... I disagree with doing that, because it hampers you from moving on with your life. Once you let go, or you have been let go of, you need to just accept it, CLOSE it, and move on. Anyone CAN do it, it is not that hard, you just have to WANT and NEED to do it.