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

Archive it. When a production closes, an Administrator can deactivate it under Administration > Production Administration: click the cog on its row and choose Deactivate Production. Step by step: Archive a production.

Archiving keeps the schedule, files and everything else. Administrators can look back through it any time (View a production's archive) and 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.