Rilsa Rael, Kingpin

Similarly, when instructed to venture into Undercity, you can't start a dungeon that isn't Undercity.

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.

The initiative is a designation a player can have. A player with the initiative designation is said to "have the initiative." The initiative carries two inherent rules. First, whenever a player takes the initiative, and at the beginning of the upkeep of the player with the initiative, that player ventures into Undercity. Second, whenever one or more creatures a player controls deal combat damage to the player who has the initiative, the first player takes the initiative. Also, some abilities will refer to having the initiative and provide other benefits.