What locks when an event is completed
Marking an event Completed does more than change a label. It freezes the event's record, so the numbers you reported stay exactly as they were.
What triggers the lock
Two things lock an event: setting its status to Completed, or archiving it (whatever its status). Cancelled does not lock an event. It only hides the event from members.
Who keeps edit access
Only two kinds of people can still change a locked event: the organization owner, and the event's owner (whoever created it, or whoever it was handed off to). Their role doesn't matter. Everyone else, including admins and the people tasks are assigned to, can view the event but not change it.
The lock covers everything under the event: its settings and options, adding, editing and completing tasks, bulk edits, budget entries and goals, RSVP numbers, ticket types and sales, sponsorships, photos and files, and adding or removing workstreams.
What stays open
Anyone who can see the event can still read everything on it and comment on its tasks, so a debrief conversation can happen right where the work was done.
Unlocking an event
The organization owner or the event's owner can unlock it. For a Completed event, open its Settings tab and change the status back to Active. For an archived event, restore it from its Settings tab or from the Archived filter on the Events page.