We investigate the dynamical behavior of physical systems near the boundary of admissibility, where the conditions required for stable physical description are only marginally satisfied. We argue that this boundary defines a distinct physical regime, which we call a selection front. Near the admissibility threshold, dynamics is governed by boundary-layer behavior characterized by large deviations, metastability, non-perturbative sensitivity to control parameters, and abrupt failure of standard effective descriptions. Perturbative effective field theory, smooth renormalization-group reasoning, and probabilistic extrapolation cease to apply even when control parameters remain small but positive. We analyze the universal features of selection fronts and explore their consequences for cosmology, black hole formation and evaporation, quantum measurement, and the limits of effective field theory. Selection fronts are shown to be generic, theory-independent features of admissibility-conditioned physics and provide a unified explanation for sharp threshold phenomena across disparate domains.