If an event "ends on" a day, does the day constitute a part of the event?
Yes, normally that last day is part of the loan agreement or contest.
This is how my library does it: an item due back on Monday can be returned or renewed any time on Monday with no fine. If returned or renewed on Tuesday, a fine is given.
For avoidance of doubt, give an explicit time for the loan to end, or use clear language explicitly stating how the last day is handled. If you check, you may find this in the small print for loans and contests.