  Local constraint in the lattice gauge theory provides an exotic mechanism
that facilitates the disorder-free localization. However, the understanding of
nonequilibrium dynamics in the non-Hermitian lattice gauge model remains
limited. Here, we investigate the quench dynamics in a system of spinless
fermions with nonreciprocal hopping in the $\mathbb{Z}_2$ gauge field. By
employing a duality mapping, we systematically explore the non-Hermitian skin
effect, localization-delocalization transition, and real-complex transition.
Through the identification of diverse scaling behaviors of quantum mutual
information for fermions and spins, we propose that the non-Hermitian quantum
disentangled liquids exist both in the localized and delocalized phases, the
former originates from the $\mathbb{Z}_2$ gauge field and the latter arises
from the non-Hermitian skin effect. Furthermore, we demonstrate that the
nonreciprocal dissipation causes the flow of quantum information. Our results
provide valuable insights into the nonequilibrium dynamics in the gauge field,
and may be experimentally validated using quantum simulators.
