A closed relationship is a relationship in which there is faithfulness and loyalty from both parties involved in the relationship. A closed relationship might also be referred to as a mutually exclusive relationship. In short, it is a monogamous relationship that does not allow the entry of extra partners or sexual/emotional relationships outside of the union.
More About Closed Relationship
A closed relationship may or may not be labeled using terms like girlfriend and boyfriend. The relationship is closed meaning that there are no new partners to be had by either party. The opposite of a closed relationship is an open relationship in which both parties agree to take other sexual partners.