The dynamics of charge-state fractions of sulfur-ion beams stripped by carbon foils at 2.0 MeV/u is investigated as a function of the initial-ion charge state q0 of the incident beam using experimental data and theoretical calculations. Experimental dependencies of the ion fractions, mean charges and equilibrium foil thicknesses on q0 are explained using the BREIT code, based on the analytical solution of the balance rate equations, as well as the ETACHA code. Experimental equilibrium charge-state distribution is qualitatively reproduced by both codes, demonstrating the capability of their approaches to the density effect. It is shown experimentally and theoretically that the non-equilibrium charge-state fractions and equilibrium foil thicknesses strongly depend on the initial ion charge q0.