  Flat bands are an ideal environment to realize unconventional electronic
phases. Here, we show that fermionic systems with dissipation governed by a
Bloch Lindbladian can realize dispersionless bands for sufficiently strong
coupling to an appropriately engineered bath. These flat bands emerge in a
"dark space" of the system-environment coupling and are long-lived by virtue of
symmetry protection from dissipation. We exhibit the robustness of this
mechanism for general one and two band models with and without spin, and
discuss conditions for their experimental realization such as in a 2D material
on a superconducting substrate.
