This note studies the robustness of nonstrong stabilizability. We consider single-input-single-output (SISO) continuous time linear systems under graph topology. A key contribution of this note is to show that there are two classes of nonstrongly stabilizable systems: One which contains plants that can be rendered strongly stabilizable by an arbitrary small perturbation, and the other which contains plants that are inherently nonstrongly stabilizable, even if perturbed. An easily implemented test referred to as weak parity interlacing property, is developed to check in which class a given model lies.