  The hallmark of symmetry-protected topological (SPT) phases is the existence
of anomalous boundary states, which can only be realized with the corresponding
bulk system. In this work, we show that for every Hermitian anomalous boundary
mode of the ten Altland-Zirnbauer classes, a non-Hermitian counterpart can be
constructed, whose long time dynamics provides a realization of the anomalous
boundary state. We prove that the non-Hermitian counterpart is characterized by
a point-gap topological invariant, and furthermore, that the invariant exactly
matches that of the corresponding Hermitian anomalous boundary mode. We thus
establish a correspondence between the topological classifications of
$(d+1)$-dimensional gapped Hermitian systems and $d$-dimensional point-gapped
non-Hermitian systems. We illustrate this general result with a number of
examples in different dimensions. This work provides a new perspective on
point-gap topological invariants in non-Hermitian systems.
