The momentum distributions of the residual nuclei after one-neutron removal have been measured in coin-cidence with gamma rays identifying the distributions associated with the excited and ground state levels of these residues. These differential partial cross sections map the momentum content of the removed-nucleon wave functions and their description rovides an exacting test of the reaction dynamics. Momentum distribu-tion data when populating the ¹⁴C and ¹⁰Be ground states show a low-high momentum asymmetry that is incompatible with the hitherto used eikonal descriptions. A fully dynamical coupled discretized continuum channels description of the elastic breakup mechanism is shown to provide an understanding of this new observation which is most pronounced for weakly bound,s-wave, nuclear halo states. This interpretation is clarified further by an analysis of the momentum distributions as a function of the angle of detection of the heavy ground state residues.