Electron stimulated desorption (ESD) of fragment ions in the energy range between 0 and 18 eV from SF6 adsorbed on rare-gas films (Kr, Xe) is reported. The ESD results are compared with previous experiments on dissociative electron attachment (DA) to gas-phase SF6. At energies characteristic for the respective rare-gas substrate strong resonant enhancements in the ESD yield of F- are observed. This enhancement is explained by the appearance of an "electron-exciton complex" in the rare-gas film (the analogue to the anionic Feshbach resonances in single atoms) which couples to the first dipole allowed excitation of the SF6 molecule. After electron and energy transfer, the highly excited SF6*(-) ion dissociates at the surface resulting in the desorption of F(-)fragments. At low electron energies tin the range from 0 to 0.6 eV) charging of the rare-gas film covered with SF6 is observed. From these experiments a charging cross section of 2.1(+/- 1.8) x 10(-15) Cm-2 is derived.