The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially-periodic potential, and subjected to non-uniform, state-dependent, damping and a bi-harmonic driving force. The contributions of the parameters of the high frequency signal to the system’s effective dissipation are examined theoretically in comparison to linearly-damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters; and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: we provide evidence of its connection to an Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.