Cult Encounter
From Arkham Horror Wiki
A Cult Encounter takes place whenever an investigator with a "One of the Thousand" Cult Membership has an encounter at the Black Cave, the Unvisited Isle, or the Woods. At that location, he or she must draw a card from the Cult Encounters deck rather than the usual encounter deck for that location.
The possibility of cult encounters was introduced in the Black Goat of the Woods expansion.