Is it possible for the earth to open up and “swallow” a person during an earthquake?

Yes. In general, ground shaking is the more familiar hazard. However, along the fault trace, for very large earthquakes, rupture can extend to the surface of the Earth and the ground on either side of the fault can move apart and then close. Anything smaller than the opening in that immediate vicinity can be shaken into the opening and sealed in when the ground closes.