  We introduce a class of one-dimensional complex optical potentials that
feature a nonlinearity-induced stability restoration, i.e., the existence of
stable nonlinear modes propagating in a waveguide whose linear eigenmodes are
unstable. The optical potential is an even function of the transverse
coordinate, i.e., the system is parity symmetric but not parity-time symmetric.
The stability restoration occurs for asymmetric stationary nonlinear modes that
do not respect the parity symmetry. Stable nonlinear states exist either for
focusing and defocusing nonlinearities. On the qualitative level the stability
restoration cab be analyzed using a simple bimodal system. Its solutions enable
systematic construction of stable stationary modes and more complex patterns
with intensity periodically oscillating along the propagation distance.
