One show closes, another opens therefore employing more people. Its rare that a theatre just sits empty.
Yes but not the same people... The cast, sound dept, automation, stage management, musicians, the crew and follow spots will no longer have jobs.
Those people aren't going to be employed on the next show... Sometimes this happens, but not as a rule. The theatre always needs crew, for example, but the requirements will change from show to show. You might need 6 or 8 members of crew for a musical and less (if any) for a play. Similarly, musicals generally require followspots plays don't.