How to stop event signups or registrations after date of event has passed?

I guess what you're really asking for here is scheduled closing of a webform. A search for that reveals #690894: Schedule form to be active/deactivate (open/close) on specific dates? where quicksketch says he won't fix it, and another user links to their Webform Scheduler project which is currently only D7. There might be other modules/snippets out there to do this kind of thing, but it looks like you might need to get your hands dirty coding, or sponsor some development. You might also want to disable the product at the same time as you close the form.

My 2 pennies!