You finish the case - one way or the other - when one of the trackers reach the end (full moon). If you finish the Case Clock first, you solved the case. If it's the Uncovered Clock, you are exposed as a werewolf and need to lay low for a while. Either way, the case is closed and for a new one you roll a new client. Of course, if you really want to keep the old client, there is nothing to stop you :)