A universal asymptotically exact theoretical approach elucidating the origin of the depletion stabilization phenomenon is developed. The theory predicts that colloidal particles in a semidilute polymer solution may be kinetically stabilized by a long-range polymer-induced repulsion. It is shown that the repulsion is due to a depletion of chain ends in the middle of the slit between solid surfaces. A nonmonotonic concentration dependence of the stabilization effect is predicted. The theory is generalized to account for surface attraction of chain ends and for polydispersity of the chains. The stabilization is enhanced for more rigid and less polydisperse chains and for the case of reversible end-adsorption.