The term that describes a person who remains in a place even though it has suffered a natural disaster is "internal displacement." However, if the individual has not relocated, they may not fit neatly into the typical definitions of displacement or migration. If the options strictly adhere to the terms listed, none perfectly describes a person who stays in their place post-disaster. If forced migration refers to individuals who are compelled to leave their homes due to disasters or conflict and "refugee" applies specifically to those who cross international borders, these terms do not directly address those who remain.
In this context, "internal displacement" is often used to describe people affected by natural disasters who may have relocated within their country but not settled elsewhere. If evaluating the best fit from the given choices, I'd suggest that "internal displacement" is the closest option.