  A many-body Wannier-Stark system coupled to an effective reservoir is studied
within a non-Hermitian approach in the presence of a periodic driving. We show
how the interplay of dissipation and driving dynamically induces a subspace of
states which are very robust against dissipation. We numerically probe the
structure of these asymptotic states and their robustness to imperfections in
the initial-state preparation and to the size of the system. Moreover, the
asymptotic states are found to be strongly entangled making them interesting
for further applications.
