Ongoing Stories are cards that have been fetched from the Story deck according to the instructions of another card (typically the outcome of a TEST or CHOICE). When they are fetched, they are placed below the cover card for Ongoing Stories, while the card that triggered fetching the Story card is placed in the Story slot of the Ship Board of the player whose turn it is. (This is later used to track who the next step of the Story belongs to.)
At the End of an Act, each card below the Ongoing Stories cover card is moved onto the card deck of the same card type (meaning having the same back, and placed perpendicular (turned sideways) there, so remind players that the card is part of an Ongoing Story. The card types are Sea Event Card, Expedition Card and Denizen Card. The next time a card is drawn from that stack, if it's drawn on the Turn of the player who has a matching card in the Story slot of their Ship Board, the Ongoing Story card is resolved immediately. Otherwise, it's placed face down in the Story slot of that player's Ship Board, and resolved the next time that player would draw a card from the same deck.