What should I do with a production when it is over?

Archive it. Under Administration > Production Administration, click the cog on the production's row and choose Deactivate Production. You'll need the Deactivate / Reactivate Production permission, which administrators usually have. Step by step: Archive a production.

Archiving keeps the schedule, files and everything else. Anyone with the View Archived Productions permission can look back through it (View a production's archive), and you can reactivate the production if the show comes back.

Before you archive, you may also want to deactivate users who were only there for this show.