In a multiplayer game, if you leave the game after Single Combat resolves but before your next turn begins, its effect lasts until your next turn would have begun. It neither expires immediately nor lasts indefinitely.

As Single Combat resolves, first the player whose turn it is chooses a creature or planeswalker they control, then each other player in turn order does the same, knowing the choices made before them. Then each unchosen creature and planeswalker is sacrificed at the same time.