725.2 There are two inherent triggered abilities associated with being the monarch. These triggered abilities have no source and are controlled by the player who was the monarch at the time the abilities triggered. This is an exception to rule 113.8. The full texts of these abilities are “At the beginning of the monarch’s end step, that player draws a card” and “Whenever a creature deals combat damage to the monarch, its controller becomes the monarch.”
725.4 If the monarch leaves the game, the active player becomes the monarch at the same time as that player leaves the game. If the active player is leaving the game or if there is no active player, the next player in turn order who can become the monarch becomes the monarch. If no player still in the game can become the monarch, the game continues with no monarch.
725.5 If the result of a continuous effect generated by a static ability is determined based on who is currently the monarch, but there is no monarch in the game as that effect begins to apply, that effect does nothing until a player becomes the monarch. See rule 613, “Continuous Effects.”