  We theoretically study the topological robustness of the surface physics
induced by Weyl Fermi-arc surface states in the presence of short-ranged
quenched disorder and surface-bulk hybridization. This is investigated with
numerically exact calculations on a lattice model exhibiting Weyl Fermi-arcs.
We find that the Fermi-arc surface states, in addition to having a finite
lifetime from disorder broadening, hybridize with nonperturbative bulk rare
states making them no longer bound to the surface (i.e. they lose their purely
surface spectral character). Thus, we provide strong numerical evidence that
the Weyl Fermi-arcs are not topologically protected from disorder. Nonetheless,
the surface chiral velocity is robust and survives in the presence of strong
disorder, persisting all the way to the Anderson-localized phase by forming
localized current loops that live within the localization length of the
surface. Thus, the Weyl semimetal is not topologically robust to the presence
of disorder, but the surface chiral velocity is.
