  We consider the defect production of a quantum system, initially prepared in
a current-carrying non-equilibrium state, during its unitary driving through a
quantum critical point. At low values of the initial current, the quantum
Kibble-Zurek scaling for the production of defects is recovered. However, at
large values of the initial current, i.e., very far from an initial equilibrium
situation, a universal scaling of the defect production is obtained which shows
an algebraic dependence with respect to the initial current value. These
scaling predictions are demonstrated by the exactly solvable Ising quantum
chain where the current-carrying state is selected through the imposition of a
Dzyaloshinskii-Moriya interaction term.
