Personal Stories were included in the Masks of Nyarlathotep expansion.
If playing with Personal Stories, the title card matching the player's Investigator is dealt out with the starting Assets. When either the "Reward" or "Consequence" condition is met, the player discards the title card and takes the resulting reward or title, resolving any of its effects immediately unless the card specifically says otherwise.
It is not possible to resolve both the Reward or Consequence. Once the first one is resolved, the title card is discarded.
Personal Stories, Rewards, and Consequences are not considered Possessions and may not be traded or discarded by any means except by the effects of the cards themselves. They otherwise follow the effects of the game.
If the player is playing a campaign, Personal Stories that have already been resolved begin the game resolved.