  Spiral spin liquids are correlated states of matter in which a frustrated
magnetic system evades order by fluctuating between a set of (nearly)
degenerate spin spirals. Here, we investigate the response of spiral spin
liquids to quenched disorder in a $J_1$-$J_2$ honeycomb-lattice Heisenberg
model. At the single-impurity level, we identify different
order-by-quenched-disorder phenomena and analyze the ensuing spin textures. In
particular, we show that the latter generally display Friedel-like
oscillations, which encode direct information about the spiral contour, i.e.,
the classical ground-state manifold. At finite defect concentrations, we
perform extensive numerical simulations and characterize the resulting phases
at zero temperature. As a result, we find that the competition between
incompatible order-by-quenched-disorder mechanisms can lead to spiral spin
glass states already at low to moderate disorder. Finally, we discuss
extensions of our conclusions to nonzero temperatures and higher-dimensional
systems, as well as their applications to experiments.
