The fuel pump draws a suction from the gas tank. As the level of fuel in the tank is decreased the suction becomes strong enough to draw the ping pong ball to the fuel line. When that occurs the flow of fuel is interrupted and the engine dies. As soon as the fuel pump stops, the suction is also stopped and the ball is released. Fuel then can be again drawn into the fuel line. It only works when you are very low on fuel, which happens a lot when you’re 17, or so.
A good story, but not possible in a stock configuration ‘55 Chevy. The fuel pickup has a sock screen on the end. It would be impossible for a ping pong ball to obstruct the line.
(disclaimer: I own several 55-57 Chevys)