I know in the past, there were always "alternates" around, but they can always take an alternate and give them a slot in a regular game at the next tape date. They tape several days a week, 5 shows per day. The theme weeks can always be done first so those that didn't make it due to time restrictions can just be a regular contestant.
The show doesn't need to announce that record holder mr. alternate was originally slated to be part of that week.