Actually, it all depends on how the both parties in the relationship decided to call it quit. In some instances, closure becomes inevitable as it would help either of the persons to know where he/she belongs, thus giving peace and serenity to them, instead of leaving them hanging, and not knowing their fate.
Other times, closure is not needed, especially if there were so much rancour surrounding the end of the relationship. This could be experienced when one of the couples just decided to call it it's over without prior knowledge of the other. And this would definitely lead to lack of closure, as the affected person would feel hurt and disappointed.
But whichever way a relationship ends, be it through closure or lack of it, there shouldn't be bad blood between the two parties, because burning of bridges is not ideal in human relationships.