Overwatch – Where to Find Brawl Stats in Overwatch

As soon as the timer ends, so when the slow down starts and the Victory/Defeat message appears.

Source : if you're about to get a level, as soon as the game ends, if you pause, you should be able to see the "Open Loot Box" option.

No.

As Иво Недев pointed out, this mechanic is to prevent you from leaving too many games before the match is over, thus negatively impacting the rest of your team.

A game is considered completed when the gameplay stops after the "Victory" or "Defeat" splash has faded, and it shows the winning team's victory line-up. Leaving at or after that point does not count towards your leaving before completion tally. Similarly, leaving in the 45 second Assemble period where you can only select a hero does not affect your tally either, as the game has not started yet.

The long and short of it is unless you are playing on a very unstable connection, or deliberately leave games before it is over, you do not need to worry about this statistic, as it is not aimed at penalizing regular play.