I'm sitting in an airport right now, and cannot get to my production sites to check but there used to be a setting in Admin panel -> Settings -> Systems -> Tickets that was something like "re-assign on reopen" or something similar to that. And so if you ahve that checked it will re-assign the ticket t the person that closed it. if not then I would think that it would become unassigned. Take a look and see if you can find it.
If not then I should be somwhere I can look again tomorrow, just let me know.