Closure is not a reality in all cases of love and loss.
As a practicing psychotherapist for 22 years, I can tell you that the concept of closure is a myth, especially in intimate relationships. There is no real way to have closure on a part of our lives that people touch, but we can still learn how to move on. Every time we interact with someone, especially in an intimate way, they leave an indelible mark on us. This could be a wonderful thing or terribly hurtful and damaging.
First let's define intimate and what intimacy means. No folks, it is not just about having sex. This is a common misconception
According to Wikipedia, an intimate relationship is an "interpersonal relationship that involves physical or emotional intimacy. Intimate relationships play a central role in the overall human experience. Humans have a general desire to belong and to love, which is usually satisfied within an intimate relationship. These relationships involve feelings of liking or loving one or more people, romance, physical or sexual attraction, sexual relationships, or emotional and personal support between the members. Intimate relationships allow a social network for people to form strong emotional attachments."
Think of yourself as a suit of armor and whenever you interact with another on an intimate level that armor is affected by dents and dings, again some good some bad. The suit of armor will never be the same. Now if you don't want to affect your suit of armor, it would only be possible if you did not engage with anyone in a personal, loving way. It is kind of like being a Hermit of Love.
Any interaction in an emotional way that involves support, like or love, or any type of sexual attraction or sexual relationship leaves you open to developing these dings and dents. This is the very thing that defines you. You are truly vulnerable.
Vulnerability is tricky because you can never really obtain a healthy loving relationship without being vulnerable or as I call it "being naked." It is a risk. The risk of being hurt, humiliated, judged, saddened, and the list goes on. However the risk can also come with love, kindness, warmth, compassion, and that list too goes on. With any risk comes the possibility of reward.
Now on the flip side if you do not take the risk and protect your suit of armor you may not become the person someone else may love with all of those funky dings and dents. You may not find love. This is your choice.
Closure or the need for closure is defined by Wikipedia as "psychological terms that describe an individual's desire for a firm answer to a question and an aversion toward ambiguity." Well, wouldn't that be nice, if we got firm answers to questions we have floating around out there in the universe. It is just not terribly realistic and questions you have may not ever be answered without any doubt involved.
You can absolutely move on from a relationship and not have closure. You can understand the dents and dings that you have received as a result of the relationship, determine if there is something of value to learn and engage in other relationships that are healthy and fulfilling. We do this stuff every day.
People break up and move on to other satisfying or not so satisfying relationships but here is the kicker…your dents and dings are what make you the person that you are. They are the good, the bad and the ugly. Don't ignore them, gain knowledge from them. Understand that they have a right to be there. Acknowledge them. Learn from them. Understand them. Respect them. They are you.