The leave edit is a rarely-used improvisational edit.
Rather than employing some kind of overt theatrical device to end a scene, the leave edit simply means exiting the stage to indicate that a scene is over.
The leave edit is perhaps utilized most in Monoscenes, a longform form that prevents improvisers from leaving a given place and time. In order to have more than one "scene" within this larger scene, improvisers will often use characters' entrances and exits to divide up the show.
The Macroscene hinges upon the leave edit, as it is essentially a mobile monoscene. The show physically follows exiting characters.