  A dissipative method that allows to access family of phantom Bethe-states
(PBS) of boundary driven XXZ spin chains, is introduced. The method consists in
coupling the ends of the open spin chain to suitable dissipative magnetic baths
to force the edge spins to satisfy specific boundary conditions necessary for
the PBS existence. Cumulative monotonous depopulation of the non-chiral
components of the density matrix with growing dissipation amplitude is
analogous to the depopulation of high-energy states in response to thermal
cooling. Compared to generic states, PBS have strong chirality, nontrivial
topology and carry high spin currents.
