In the game of Stratego, is it possible to destroy all 40 enemy units?
As Dennis_E mentioned, it is possible, but I would say it is improbable.

To destroy all enemy units, you would have to avoid the flag until the 40th capture. Additionally, one of the enemy's non-stationary pieces must be the 39th piece to be captured, and it must suicide itself on one of your pieces.  Otherwise, the game would have ended beforehand as the opponent would have been unable to move any piece during their turn, thus losing before you could destroy all 40 pieces.

What makes this improbable is that without assistance from your opponent, you would have to identify all the non-flag stationary pieces and destroy them before destroying the flag while ensuring the opponent maintains an additional non-stationary piece, which they must voluntarily throw at a piece that would destroy it on a turn preceding one where you are able to capture the flag.

I really cannot see a human opponent not forfeiting at this point unless they were colluding with you.