We introduce and investigate material junctions as a generic and tunable electronic platform for the realization of exotic non-Hermitian (NH) topological states of matter, where the NH character is induced by the surface self-energy of a thermal reservoir. As a conceptually rich and immediately experimentally realizable example, we consider a three-dimensional topological insulator (TI) coupled to a ferromagnetic lead. Remarkably, the symmetry-protected TI is promoted in a dissipative fashion to a non-symmetry-protected NH Weyl phase with no direct Hermitian counterpart and which exhibits robustness against any perturbation. The transition between a gapped phase and the NH Weyl phase may be readily tuned experimentally with the magnetization direction of the ferromagnetic lead. Given the robustness of this exotic nodal phase, our general analysis also applies to, e.g., a two-dimensional electron gas close to criticality in proximity to a ferromagnetic lead. There, the predicted bulk Fermi arcs are directly amenable to surface spectroscopy methods such as angle-resolved photoemission spectroscopy.