The term that describes a person who remains in a place even though it has suffered a natural disaster is "internal displacement." However, this typically refers to those who have been forced to move within their own country due to a disaster. If a person remains in place after such an event, that situation doesn't have a specific term among the options provided.
None of the given options are perfectly accurate for someone staying in a disaster-stricken area, but "internal displacement" is the closest term if we consider the context of natural disasters. If you're looking for a precise term for someone who stays, you might consider saying they are "remaining" or "staying" rather than using a label typically associated with displacement.