I swing at the monarch. Obviously I can't become the monarch, so the damage trigger resolves without changing the monarch. But if I kill that player, the following rule applies.
718.4. 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 becomes the monarch.
I'm the active player, so the rule tries to make me monarch but can't. Is there now no monarch in the game?
Even if there were a ruling or a rules change that made the next eligible player the monarch (I haven't seen any indication of this though), the situation would happen if everyone had their own Jared enter this turn before the monarch died.
So, is this one strange case where there stops being a monarch in the game?