  In BiS$_2$-based layered superconductors,the existence of gap nodes on
Fermi-surface curves has been suggested from angle-resolved photoemission
spectroscopy measurements, whereas the conventional $s$-wave gap has been
proposed from measurements of superfluid density and thermal conductivity. To
reconcile these two distinct experimental results of the gap node, we
investigate nonmagnetic impurity effects in the superconductor with a
disconnected pocketlike Fermi-surface structure. Then, we claim that the
seemingly contradictory situation concerning the gap node is resolved by a
concept of dirty nodal extended $s$-wave superconductivity. Provided that it is
unnecessary to consider the nodes of the gap, at first glance, the conventional
$s$-wave gap seems to be a unique solution, but in the pocketlike Fermi-surface
topology, a nontrivial possibility of a nodeless $d$-wave superconductor is
pointed out. To clarify the gap symmetry, we propose to perform experiments on
nuclear magnetic relaxation rate $T_{1}^{-1}$ in BiS$_2$-based layered
superconductors.
