We derive the major characteristics of inclusive and diffractive final states in deep-inelastic scattering off heavy nuclei for the high-energy (small-x) kinematics in which the limit of complete absorption is reached for the dominant hadronic fluctuations in the virtual photon (the black-body limit of the process). Both the longitudinal and transverse distributions of the leading hadrons are found to be strikingly different from the corresponding ones within the leading-twist approximation, and hence provide unambiguous signals for the onset of the black-body limit.