We study the proximity effect in a quantum wire with broken time-reversal symmetry connected to a superconductor. We consider the situation of a strong symmetry breaking, so that Cooper pairs entering the wire from the superconductor are immediately destroyed. Nevertheless, the proximity effect survives. The local electronic density of states is influenced by the proximity to the superconductor, provided that localization effects are taken into account. Remarkably, the sign of the effect is sensitive to the way the time-reversal symmetry is broken: In the spin-symmetric case (orbital magnetic field), the density of states is depleted near the Fermi energy, whereas for the broken spin symmetry (magnetic impurities), the density of states is enhanced. In the latter case, our results directly apply to the topological superconductor hosting a Majorana fermion at the boundary. If such a superconductor is connected to the disordered wire, the Majorana fermion is spread into the wire, subject to Anderson localization. Our calculation yields the local density of states in the normal wire including the spatial profile of the Majorana mode and the depletion of the local density of other low-energy states.