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Animal excursions out of protected areas are a source of human-wildlife conflict and can lead animals into ecological traps. These arise when animals prefer areas of their habitat conferring lower fitness than other available areas. Ecological traps should become increasingly common as humans continue to alter habitats, yet their impact on population viability has rarely been documented and there is limited knowledge on how to disarm them. Moreover, although spatial factors such as the proportion of trap habitat in the landscape are crucial in determining the probability of extinction, few studies have attempted to link animal use of space to demography to obtain insights into how to release trapped populations. Here we tackle these gaps using a stochastic, spatially explicit matrix model parametrized with empirical data. We show that a free-ranging population of plains bison (Bison bison bison) caught in an ecological trap caused by legal but unregulated hunting has a 66% probability of extinction over the next 50 years under current conditions. By linking the time bison spent in fields with hunting permission to survival and population persistence, we show that bison use of such fields must decrease by 70% to ensure population viability. Our approach narrowed down the ecological trap to < 1% of the population's range during the hunting period. Targeting this limited portion of the landscape would hence be a cost-effective strategy to disarm the trap. We show that a spatially explicit approach to demography can refine conservation strategies to avoid potentially onerous and ineffective interventions.