Most relationships where one person is very possessive usually equates to a bad relationship. I don’t think there are happy relationships where one is overly possessive. At the beginning of the relationship, the couple may not be worried about one of them being overly possessive.
However, after a few weeks or months, the man or woman might get tired of being possessed by their significant other. Being overly possessive does ruin a good and happy relationship. The person will need help in learning to back off and give that person space. One way to do this is to seek help from a therapist. This therapist will give them good ideas to stop being possessive. Finding other interests will help make them less possessive.