If the person who did not want the divorce meets someone new, they can not have that relationship until there is an annulment. If they have a relationship without an annulment then they are out of the communion of the church. I have dealt with this with friends. It’s devastating. If my husband divorced me, I would stay single and not in a relationship.
What happens in the case where the person who initiated the divorce meets someone and wants to remarry? Do they not have the right to petition for annulment?