Stochastic overflow, as discussed by Carl Sagan in "The Demon-Haunted World," refers to a theoretical phenomenon where an event, despite being highly improbable, could occur given enough time. Sagan illustrates this concept with the example of a car potentially passing through a wall and appearing on the street, contingent on conditions that exceed the universe's age. He emphasizes that while the average waiting time for such an event is vastly longer than the universe's existence, it remains a possibility. This idea highlights the intersection of probability and physics in understanding seemingly impossible scenarios. Overall, stochastic overflow serves as a thought experiment about the limits of chance and the nature of reality.