After a break-up, closure from the past relationship allows you to let go of resentments, and to look normally at that event of your life and not in bold font.
If you feel your relationship can work even after the breakup you may consider taking help of relationship counseling or online relationship counseling if you are not comfortable in facing the person personally. A relationship counselor will either help you mend your relationship or will help you find out what went wrong so that end of the day you both can be at peace and get a closure.