  Being motivated by intriguing phenomena such as the breakdown of conventional
bulk boundary correspondence and emergence of skin modes in the context of
non-Hermitian (NH) topological insulators, we here propose a NH second-order
topological superconductor (SOTSC) model that hosts Majorana zero modes (MZMs).
Employing the non-Bloch form of NH Hamiltonian, we topologically characterize
the above modes by biorthogonal nested polarization and resolve the apparent
breakdown of the bulk boundary correspondence. Unlike the Hermitian SOTSC, we
notice that the MZMs inhabit only one corner out of four in the two-dimensional
NH SOTSC. We extend the static MZMs into the realm of Floquet drive. We find
anomalous $\pi$-mode following low-frequency mass-kick in addition to the
regular $0$-mode that is usually engineered in a high-frequency regime. We
further characterize the regular $0$-mode with biorthogonal Floquet nested
polarization. Our proposal is not limited to the $d$-wave superconductivity
only and can be realized in the experiment with strongly correlated optical
lattice platforms.
