This paper clarifies the logical status of masslessness in relativistic physics by identifying it as a structural classification rather than a dynamical property or a symmetry-protected feature. Adopting the standard Lorentz-invariant definition of mass, the analysis introduces identifiability as the capacity of a physical system to be invariantly tracked along its evolution via proper time and internal degrees of freedom. It is shown that any physically admissible system that lacks identifiability cannot be associated with a time-like worldline and is therefore necessarily null, forcing its Lorentz invariant to vanish. Conversely, systems that admit identifiability are structurally excluded from the null sector and cannot be massless. This yields a rigid and exhaustive classification that simultaneously explains known massless systems and rules out entire classes of hypothetical massless entities. The result does not rely on specific dynamics or symmetry arguments and sharply constrains model-building strategies.