We investigate ultrathin superconducting TiN films, which are very close to the localization threshold. Perpendicular magnetic field drives the films from the superconducting to an insulating state, with very high resistance. Further increase of the magnetic field leads to an exponential decay of the resistance towards a finite value. In the limit of low temperatures, the saturation value can be very accurately extrapolated to the universal quantum resistance h/e(2). Our analysis suggests that at high magnetic fields a new ground state, distinct from the normal metallic state occurring above the superconducting transition temperature, is formed. A comparison with other studies on different materials indicates that the quantum metallic phase following the magnetic-field-induced insulating phase is a generic property of systems close to the disorder-driven superconductor-insulator transition.