Shelters serve as critical facilities where people gather during and after hurricanes. A basic requirement of 'operation' for a shelter is being functional and available to help. However, what happens when shelters themselves are damaged and unable to serve those people? An open question with key policy implications is: How can we identify the most critical shelter(s) as a part of broader emergency evacuation operations and how can we respond to an interdiction? This paper develops a two-step modeling framework consisting of enhanced r-interdiction median models (RIM) to identify the most significant shelter(s) and revised p-median models to identify shelters to repurpose during such an interdiction where shelters are rendered off-line. Proposed models are applied on a Southeast Florida case study with respect to scenarios based on varying hurricane strength and shelter demand. Findings indicate that models are susceptible to travel cost variation based on the demand-weighted objectives, and that shelter selections vary due to different demand scenarios created which focus on different population segments. As hurricane strength increases, critical shelter identification is driven by flooding and storm surge risks. These findings can inform efforts to harden those critical shelters so that they can better serve populations in need.