Close it on purpose, and clean up after
The habits that make a closed page kind are set earlier. Choose which ending you mean while building โ the seat limit, a cut-off you keep, or simply the start time โ and write the date into the description only if you will honour it. Put the next date on its own page before the current one passes, so the late arrival's reply can name a real address.
Then do the quiet housekeeping. The attendee list outlives the page: cancelled and no-show statuses keep the record honest, the export travels to whoever needs it, and the reminder switches stop mattering on their own. A closed page is not the end of the registration product; it is the last screen of it, and the only one most of the queue will ever see.