The NPC of the player just stands there in idle mode.

Someone walks up, says "Dungeoncrawl with me?"

The NPC checks its list of friends and settings - crawl with anyone, crawl with noone, crawl with these people only, crawl with kingdom members only - and decides to enter Crawl mode.

The player logs off, five minutes later the NPC returns to idle mode.

Or the player leaves the dungeon, the NPC stays and returns to idle mode.

It all depends on how the player sets his offline AI