The countdown reached zero and the mode is still on

Settings → Switch off automatically at that time is switched off. With it off the clock runs out and the mode waits for you. Switching it on and saving then switches the mode off with the save, and asks first whether to email the people waiting. If the countdown ended more than a week ago, the save asks nothing and emails nobody, and the message after it says so: send the launch email from the Subscribers screen if you still want to.

With it on, visitors see your site from that time whether or not your host's cron ever runs, because the time is compared on every request as well as scheduled. Switching the mode off in the settings, and the launch email, wait for WordPress cron, which usually runs on the next visit. If that is more than a week after the time, the mode is switched off and nobody is emailed; the Dashboard offers Send the launch email instead. Until then the Dashboard says the scheduled switch-off time has passed. Saving a screen in the meantime does not cancel it, unless the save moves the switch-off time, turns Switch off automatically at that time off, or switches the mode on again with Enable; open a page or two of your site and it runs. Saving Shop closed for orders on the Page screen, or importing a settings file that switches the mode off, in the meantime is your launch instead: nobody is emailed by it, and the message after it says so. So is a Settings save or a Disable press where you answered the question about the launch email: the mode is switched off there and then, and the list is emailed only if you said yes. A Settings save made more than a week after that time switches the mode off and emails nobody, however long cron has been waiting.

A Switch off at time that had already passed when you typed it does not wait for cron: saving it switches the mode off there and then, and the message after the save says so. The exception is the wait above: if an earlier switch-off time had passed and its scheduled switch-off is still to run, a save that asked you nothing leaves it to run. So does any save of the Settings screen while the mode is still on after its switch-off time with nothing scheduled to switch it off, which can happen when a scheduled task is lost: the message after it also says how many people were not emailed.