in the Problem Management project, there's a filter component called "Filter Out Closed & Resolved Incidents" that is removing any closed incidents from the search when you click to "Add Incident" and then "Search For" an incident. I can't recall if that project is locked out or not. If it is locked out, you may be out of luck (in a supportable sense). If not, you can just route around or otherwise disable that filter so that search results include closed tickets.
I've never actually done what you're asking, so I'm not sure if there are any reference ties that may be broken or won't work because the incidents are closed.