  We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring
exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH
physics naturally arises from the self-energy in a disorder-averaged Green's
function description. Notably, we find that at least two nodal points in the
clean Hermitian system are required for exceptional points to be effectively
stabilized upon adding disorder. We identify and study experimental signatures
of our theoretical findings both in the spectral functions and in mesoscopic
quantum transport properties of the considered systems. Our results are
quantitatively corroborated and exemplified by numerically exact simulations on
a microscopic lattice model. The proposed setting provides a conceptually
minimal framework for the realization and study of topological NH phases in
quantum many-body systems.
