  As a continuation of our previous work on the conservation and breaking of
the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320
(2023)}], in this work, the PSS in nuclear single-particle bound and resonant
states are investigated uniformly within a relativistic framework by exploring
the poles of the Green's function in spherical Woods-Saxon potentials. As the
potential depths increase from zero to finite depths, the PS partners evolve
from resonant states to bound states. In this progress,the PSS is broken
gradually with energy, width, and density splittings. Specially, the energy and
width splittings for the resonant and bound states are directly determined by
the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious
threshold effect is observed for the energy splitting at a critical potential
depth, with which the PS partners locate between the centrifugal barriers of PS
partners. The differences in the density distributions of the lower component
between the PS partners are manifested in the phase shift for the resonant
states and amplitudes for bound states. Besides, the evolution of the phase
shift as the potential depth is consistent with those for the width splitting.
