There is a 'Date Completed' field listed for the Phone Call Record Type {completeddate}.

If you create an Activity Saved Search then this field displays for Phone Calls, Events and Tasks. For Events it displays the Date that the Event was marked Completed (as shown in System Notes).

However, we would like to update the Date Completed (as we have found a large number of old Events that were not completed at the time.

I cannot find any way to update the 'Date Completed' field on an Event (by editing, CSV importing, or by script). Looking on the Record Browser, Date Completed is not shown as a valid field on Events or Tasks (only Phone Calls) - but somehow a date is shown on an Activity Search for Events and Tasks (and it appears to be the actual date/time the status changed to completed).