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We refer to systems violating the conditions for structurally stable regulation as critical. At least one of the following must fail at a critical system: asymptotic rejection of the exogenous system, stabilization of the closed-loop system, or structural stability. This has not been explicitly addressed. We show that any structurally stable regulator is necessarily destabilizing when applied to a critical system, that destabilization is linked to structural stability, and we characterize the resulting unstable poles.