  In this paper, we systematically investigate the impurity-induced bound
states in 1D non-Hermitian systems. By establishing an exact relationship
between impurity potential and bound-state energy, we determine the minimum
impurity potential required to generate bound states within each point energy
gap. We demonstrate that the absence of Bloch saddle points necessitates a
finite threshold of impurity potential; otherwise, infinitesimal impurity
potential can create bound states. Furthermore, we show that the bound states
residing in the point gaps with nonzero spectral winding exhibit sensitivity to
boundary conditions and will be squeezed towards the edges when the boundaries
are opened, indicating the bulk-boundary correspondence in terms of point-gap
topology.
