Using density functional electronic structure calculations, we establish the consequences of surface termination and modification on protected surface states of metacinnabar (β-HgS). Whereas we find that the Dirac cone is isotropic and well separated from the valence band for the (110) surface, it is highly anisotropic at the pure (001) surface. We demonstrate that the anisotropy is modified by surface passivation because the topological surface states include contributions from dangling bonds. Such dangling bonds exist on all pure surfaces within the whole class HgX with X=S, Se, or Te and directly affect the properties of the Dirac cone. Surface modifications also alter the spatial location (depth and decay length) of the topologically protected edge states, which renders them essential for the interpretation of photoemission data.