Resonant tunneling of electrons through a dissipative barrier is studied within a generalized spin-boson model. The model accounts for a nonlinear inelastic coupling between the electron and harmonic (bath) nuclear modes inside the barrier. In particular, we study the case in which the nuclear frequencies are similar to the decay rate of the electronic resonance states, as may appear in electron transport through narrow molecular barriers. Two cases are considered. In the case of a single responsive mode numerically exact wave-packet dynamics shows that the inelastic coupling increases the time delay of the tunneling electron in the barrier and the decay process out of the barrier is characterized by nonexponential steps. In the case of a multimode (Ohmic) bath an approximate treatment of the dynamics, based on temperature dependent nonlinear Langevin-Schrodinger equations, implies that the trapped electron wavepacket is fully solvated in the barrier due to irreversible dissipation at low temperatures. An interpretation of the solvation process in terms of the mean-field approximation is given and discussed.