An ever larger proportion of Earth's biota is affected by the current accelerating environmental change. The mismatches between organisms and their environments are now increasing in both magnitude and frequency, resulting in lowered fitness and hence the decline of populations. Under this scenario, species with behavioral and/or physiological traits that provide them shelter from the environment are predicted to be less vulnerable to population declines than species that are always exposed to the elements. Here, we coded 4,536 living mammal species for sleep-or-hide (SLOH) behavior, including hibernation, torpor, and the use of burrows, among other related traits. We demonstrate that species that exhibit SLOH behavior are underrepresented in high-risk International Union for Conservation of Nature Red List categories. We found that SLOH behavior contributes to lowering extinction risk even after we accounted for other factors that directly or indirectly buffer species against extinction, such as larger geographic ranges and smaller body sizes. This result is robust to analyses using phylogenetically independent contrasts. Sleep-or-hide behavior, made possible by a related suite of physiological adaptations, allows mammals to function at lower metabolic rates and/or buffer them from changing physical elements. Mammals with SLOH behavior have a greater propensity to survive in the current extinction crisis and probably also in past crises because of reduced exposure to environmental stress.