We consider the effects of strong light-matter interaction on electronic friction in molecular junctions within the generic model of a single molecule nanocavity junction. Results of the Hubbard nonequilibrium Green function (NEGF) simulations are compared with mean-field NEGF and generalized Head-Gordon and Tully (HGT) approaches. Mean-field NEGF is shown to fail qualitatively at strong intrasystem interactions, while accuracy of the generalized HGT results is restricted to situations of well separated intramolecular excitations when bath induced coherences are negligible. Numerical results show effects of bias and cavity mode pumping on electronic friction. We demonstrate nonmonotonic behavior of the friction on the bias and intensity of the pumping field and indicate possibility of engineering friction control in single molecule junctions.