  The unusual surface states of topological semimetals have attracted a lot of
attention. Recently, we showed [PNAS 113, 8648 (2016)] that for a Dirac
semimetal (DSM) arising from band-inversion, such as Na$_3$Bi and Cd$_3$As$_2$,
the expected double Fermi arcs on the surface are not topologically protected.
Quite generally, the arcs deform into states similar to those on the surface of
a strong topological insulator. Here we address two questions related to
deformation and stability of surface states in DSMs. First, we discuss why
certain perturbations, no matter how large, are unable to destroy the double
Fermi arcs. We show that this is related to certain extra (particle-hole)
symmetry, which is non-generic in materials. Second, we discuss situations in
which the surface states are completely destroyed without breaking any symmetry
or impacting the bulk Dirac nodes. We are not aware of any experimental or
density functional theory (DFT) candidates for a material which is a bulk DSM
without any surface states, but our results clearly show that this is possible.
