  We demonstrate that dislocations in two-dimensional non-Hermitian systems can
give rise to density accumulation or depletion through the localization of an
extensive number of states. These effects are shown by numerical simulations in
a prototype lattice model and expose a different face of non-Hermitian skin
effect, by disentangling it from the need for boundaries. We identify a
topological invariant responsible for the dislocation skin effect, which takes
the form of a ${\mathbb Z}_2$ Hopf index that depends on the Burgers vector
characterizing the dislocations. Remarkably, we find that this effect and its
corresponding signature for defects in Hermitian systems falls outside of the
known topological classification based on bulk-defect correspondence.
