Currently, when we vote to close a question as being a duplicate it provides a comment with a link to the duplicate question. The OP then has the option to follow that link to review the question.
As it stands, a question requires 5 votes to close (though I assume admins/mods can close as duplicate immediately?). The problem with requiring 5 votes is that a question might not always get all 5 votes.
Now, this is good from the point of view that we want multiple reputable people to agree it should be closed. But there are likely some instances (I would assume quite a few) where a question has been voted as duplicate, but not enough times to close. However, the OP may have already reviewed the possible duplicate, found it to be a match (and therefore solved their problem), but we are still stuck with an open, unanswered duplicate that the OP doesn't care about anymore.
So my proposition is to have a feature that allows the OP to say "I confirm this is a duplicate, my problem has been solved, this question can be closed". This could be an option that only becomes available once a duplicate vote has been logged. If multiple questions are identified as duplicates, then the OP should select which one was the one that solved their problem so the closed question can be correctly linked.