Feywild Caretaker

If the player with the initiative leaves the game, the active player takes the initiative at the same time 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 takes the initiative.

There is no initiative in a game until an effect instructs a player to take the initiative. Once a player is instructed to do this, they have the initiative until another player takes the initiative.

If you’re already in a dungeon when instructed to venture into Undercity, you move to the next room of that dungeon. If you are already in the last room, you will complete that dungeon and start Undercity. This is true whether you’re already in Undercity or any other dungeon.