  The topology of non-Hermitian systems is fundamentally changed by the
non-Hermitian skin effect, which leads to the generalized bulk-boundary
correspondence. Based on the non-Bloch band theory, we get insight into the
interplay between the non-Hermiticity and the second-order topological
superconductors in two spatial dimensions. We investigate that the
non-Hermiticity drives both the bulk states and topological edge modes to
accumulate toward opposite corners of the system depending on the particle and
hole degrees of freedom protected by the particle-hole symmetry. Furthermore,
the degeneracy of the Majorana corner modes can be broken in terms of both the
eigenenergies and the eigenstates. Through an edge theory analysis, we
elucidate the impact of non-Hermiticity and enable the extension of
higher-order topological superconductors to the realm of non-Hermitian systems.
We show that $Z_2$ skin effect and $Z_2$ skin-topological modes reveal the
universal characteristics of non-Hermitian second-order topological
superconductors and the generalized bulk-boundary correspondence is further
enriched by the particle-hole symmetry.
