Desorption of positive ions in alkali halides resulting from the repulsive environment created by core-hole Auger decay has been previously found not likely due to lattice rearrangement and trapping of the ion. We revisit the problem by studying ion trajectories using classical molecular dynamics in the crystalline (rather than cluster) geometry with careful account of the Madelung energy. We find that the previous findings remain unchanged. In contrast to previous works, we also assume that the positive ion gained substantial amount of kinetic energy at the onset of simulations, crudely mimicking ion-stimulated desorption. Then the ejection of the formed positive halogen ion occurs for initial kinetic energies of the order 2 eV forNaFand 0.65 eV forLiF. Implications for viability of the Knotek-Feibelman mechanism are discussed.