Current trends in laser technology have reached the regime of studying atoms stabilized against ionization, going beyond the perturbation theory. In this work, properties of a laser-dressed sulfur atom are examined in this stabilization regime. The electronic structure of a sulfur atom changes dramatically as it interacts with strong high-frequency laser fields. Degenerate molecularlike states are obtained for the ground state triplet of the laser-dressed sulfur atom for high-frequency and moderate intensity laser parameters. The degenerate ground state is obtained for a laser intensity which is smaller by more than one order of magnitude than the intensity required for hydrogen atoms due to many electron screening effects. An infinitesimally weak static field mixes these degenerate states to give rise to asymmetric states with large permanent dipole moments. Hence, a strong linear Stark effect rather than the usual quadratic one is obtained.