Topological materials have unusual surface spin properties including a net surface spin current protected by the bulk symmetry properties. When such materials are reduced to thin films, their gapless spin-polarized surface states must connect, by analytic continuation, to bulk-derived quantum-well states, which are spin-unpolarized in centrosymmetric systems. The nature of this passage in a model system, Sb films, is investigated. Angle-resolved photoemission shows a smooth transition, while calculations elucidate the correlated evolution of the spin and charge distributions in real space.