ENDOR measurements on the ¹⁹F^- nuclei in the first four shells of KZnF₃ containing Dy³⁺ ions in the cubic site are reported. The values and signs of the hyperfine and transferred hyperfine interaction parameters are determined. The local deformation of the crystal lattice in the vicinity of the impurity ion is estimated. The theoretical analysis of the THFI parameters for the first coordination shell of the F^- ions has been carried out. For the Dy³⁺ ion the influence of spin polarization of the closed 5s and 5p shells is considered for the first time. Spin polarization is shown to play a significant role in the mechanism of rare-earth ion-ligand coupling.