We introduce a solvable model of driven fermions that elucidates the role of the localization transition in driven disordered magnets, as used in the context of dynamic nuclear polarization. Instead of spins, we study a set of noninteracting fermions that are coupled locally to nuclear spins and tend to hyperpolarize them. The induced hyperpolarization is a fingerprint of the driven steady state of the fermions, which undergo an Anderson localization (AL) transition upon increasing the disorder. Our central result is that the maximal hyperpolarization level is always found close to the localization transition. In the limit of small nuclear moments the maximum is pinned to the transition, and the hyperpolarization is strongly enhanced by multifractal correlations in the critical state of the nearly localized driven system, its magnitude reflecting multifractal scaling.