  Anomalous surface states with Fermi arcs are commonly considered to be a
fingerprint of Dirac semimetals (DSMs). In contrast to Weyl semimetals,
however, Fermi arcs of DSMs are not topologically protected. Using
first-principles calculations, we predict that $\beta$-CuI is a peculiar DSM
whose surface states form closed Fermi pockets instead of Fermi arcs. In such a
fermiological Dirac semimetal, the deformation mechanism from Fermi arcs to
Fermi pockets stems from a large cubic term preserving all crystal symmetries,
and the small energy difference between the surface and bulk Dirac points. The
cubic term in $\beta$-CuI, usually negligible in prototypical DSMs, becomes
relevant because of the particular crystal structure. As such, we establish a
concrete material example manifesting the lack of topological protection for
surface Fermi arcs in DSMs
