Due to some turn-over, some reviews are not being closed and there appears to be no way to join the review. Is there some sort of back-door way for an admin to keep the review list cleared?
Please have a look at Administration > Security Settings > Permission Schemes. Here you will find which users/groups are allowed to close a review.
Also, look at Project Settings > Projects > (project key) > Permission scheme to find out which permission scheme is used in the project.