Willful attacks or natural disasters pose extreme risks to sectors of the economy. An extreme-event analysis extension is proposed for the Inoperability Input-Output Model (IIM) and the Dynamic IIM (DIIM), which are analytical methodologies for assessing the propagated consequences of initial disruptions to a set of sectors. The article discusses two major risk categories that the economy typically experiences following extreme events: (i) significant changes in consumption patterns due to lingering public fear and (ii) adjustments to the production outputs of the interdependent economic sectors that are necessary to match prevailing consumption levels during the recovery period. Probability distributions associated with changes in the consumption of directly affected sectors are generated based on trends, forecasts, and expert evidence to assess the expected losses of the economy. Analytical formulations are derived to quantify the extreme risks associated with a set of initially affected sectors. In addition, Monte Carlo simulation is used to handle the more complex calculations required for a larger set of sectors and general types of probability distributions. A two-sector example is provided at the end of the article to illustrate the proposed extreme risk model formulations.