Several experiments suggest that the charge carriers in the normal state of certain cuprate superconductors reside on domain walls. In an earlier paper, we suggested that several aspects of the anomalous dynamical behavior of these materials could be explained, at least qualitatively, on this basis. Here, using results on the ground state energy of the 1-dimensional Hubbard model (soluble by Bethe ansatz techniques) as a function of charge density, we argue that a non-zero charge density localized to domain walls is a very plausible consequence of strong electron-electron repulsion. We also suggest a method to suppress meandering of the walls, and thereby enhance their signature in neutron diffraction.