If a player leaves the game during their turn, that turn continues to its completion without an active player. If the active player would receive priority, instead the next player in turn order receives priority, or the top object on the stack resolves, or the phase or step ends, whichever is appropriate.
May 3, 2019 · War of the Spark
If a player who has left the game would begin a turn, that turn doesn’t begin.
January 25, 2019 · Ravnica Allegiance
If a player who has left the game would begin a turn, that turn doesn't begin.
June 5, 2017 · Commander Anthology
If a player who has left the game would begin a turn, that turn doesn’t begin.
July 22, 2016 · Eldritch Moon
When a player leaves the game, any continuous effects with durations that last until that player’s next turn or until a specific point in that turn will last until that turn would have begun. They neither expire immediately nor last indefinitely.
May 1, 2014 · Journey into Nyx
When a player leaves the game, objects that player owns in the ante zone do not leave the game. This is an exception to rule 800.4a. See rule 407, “Ante.”
May 1, 2012 · Avacyn Restored
When a player leaves the game, objects that player owns in the ante zone do not leave the game. This is an exception to rule 800.4a. See rule 407, "Ante."
February 1, 2012 · Dark Ascension
In a Planechase game, if the player designated as the planar controller would leave the game, instead the next player in turn order that wouldn't leave the game becomes the planar controller, then the old planar controller leaves the game. See rule 309.5.