  We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of
strong dissipation, described by Lindblad master equation. The nonequilibrium
steady state is expressed in terms of a matrix product ansatz using novel
site-dependent Lax operators. The components of Lax operators satisfy a simple
set of linear recurrence equations that generalize the defining algebraic
relations of the quantum group $U_q(sl_2)$. We reveal connection between the
nonequilibrium steady state of the nonunitary dynamics and the respective
integrable model with edge magnetic fields, described by coherent unitary
dynamics.
