The thing about Duck Hunt is that it doesn't have an official ending, not like traditional games of today that have sweeping cinematic masterpiece conclusions. Instead it has what is called a kill screen; once you play through 99 levels, a screen bearing the title of “Round 0” appears. In this level, the ducks begin flying erratically around the screen and cannot be targeted at all by the player. Also, the dog starts smugly laughing in the background on a loop, like a never-ending fail state.
It's a bit of a glitched-out nightmare until the end when it gives players a “game over” and restarts. The kill screen is essentially a call back to Duck Hunt‘s arcade days, as the kill screen is a common occurrence with arcade games that seemingly have no ending, like Pac-Man or Tetris. In other words, Duck Hunt doesn't really end, but it stops.