During crises like pandemics, organizations often face substantial disruptions that significantly increase job demands (JDs) on employees. This study investigates the impact of high JDs on moral disengagement (MD) and subsequent employee behaviors. Drawing upon social cognitive theory, we hypothesize that excessive JDs undermine self‐regulatory mechanisms, resulting in MD and affecting counterproductive work behavior (CWB) and extra‐role behaviors (ERBs). Additionally, we employ the conservation of resources theory to examine how family–work enrichment (FWE) can encourage ERB, potentially mitigating negative outcomes. To test our hypotheses, a two‐wave time‐lagged survey was conducted among hospital staff members during the COVID‐19 pandemic. The findings support our theoretical model, demonstrating that high JDs deactivate self‐regulatory systems, leading to MD and varied behavioral outcomes. However, FWE fosters ERB even among morally disengaged employees. This study advances the literature by elucidating the mechanisms of MD and highlighting the role of family support in promoting positive behaviors during crises. Implications for both theory and practice are discussed, offering insights for managing employee well‐being and performance in challenging times.