The beta decay of Li-11 has been investigated at TRIUMF-ISAC using a high-efficiency array of Compton suppressed HPGe detectors. From a line-shape analysis of the Doppler-broadened peaks observed in the Be-10 gamma spectrum, both the half-lives of states in Be-10 and the energies of the beta-delayed neutrons feeding those states were obtained. Furthermore, it was possible to determine the excitation energies of the parent states in Be-11 with uncertainties comparable to those obtained from neutron spectroscopy experiments. These data suggest that the beta decay to the 8.81 MeV state in Be-11 occurs in the Li-9 core and that one neutron comprising the halo of Li-11 survives in a halolike configuration after the beta-delayed neutron emission from this level.