  The phase diagram of a spin-orbit-coupled two-component Bose gas includes a
supersolid stripe phase, which is featuring density modulations along the
direction of the spin-orbit coupling. This phase has been recently found
experimentally [J.~Li \textit{et al.}, Nature (London) \textbf{543}, 91
(2017)]. In the present work we characterize the superfluid behavior of the
stripe phase by calculating the drag force acting on a moving impurity. Because
of the gapless band structure of the excitation spectrum, the Landau critical
velocity vanishes if the motion is not strictly parallel to the stripes, and
energy dissipation takes place at any speed. Moreover, due to the spin-orbit
coupling, the drag force can develop a component perpendicular to the velocity
of the impurity. Finally, by estimating the time over which the energy
dissipation occurs, we find that for slow impurities the effects of friction
are negligible on a time scale up to several seconds, which is comparable with
the duration of a typical experiment.
