We report on the single neutron and proton removal reactions from unstable nuclei with large asymmetry ΔS = S(n)-S(p) at incident energies below 80 MeV/nucleon. Strong nonsudden effects are observed in the case of deeply-bound-nucleon removal. The corresponding parallel momentum distributions exhibit an abrupt cutoff at high momentum that corresponds to an energy threshold occurring when the incident energy per particle is of comparable magnitude to the nucleon separation energy. A large low-momentum tail is related to both dissipative processes and the dynamics of the nucleon removal process. New limits for the applicability of the sudden and eikonal approximations in nucleon knockout are given.