  We consider the Quantum Null Energy Condition (QNEC) for holographic
conformal field theories in two spacetime dimensions (CFT$_2$). We show that
QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein
gravity, including systems that are far from thermal equilibrium. If the
Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be
saturated, whereby we give both analytical and numerical examples. In
particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries
we find a curious half-saturation of QNEC for large entangling regions. We also
address order one corrections from quantum backreactions of a scalar field in
AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge
expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface
part and the bulk entanglement contribution to EE and QNEC. At leading order
for small entangling regions the contribution from bulk EE exactly cancels the
contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders
in the size of the region the contributions are almost equal while QNEC is not
saturated. For a half-space entangling region we find that QNEC is gapped by
$h/4$ in the large $h$ expansion.
