Electrolyte gating with ionic liquids is a powerful tool for inducing novel conducting phases in correlated insulators. An archetypal correlated material is vanadium dioxide (VO2), which is insulating only at temperatures below a characteristic phase transition temperature. We show that electrolyte gating of epitaxial thin films of VO2 suppresses the metal-to-insulator transition and stabilizes the metallic phase to temperatures below 5 kelvin, even after the ionic liquid is completely removed. We found that electrolyte gating of VO2 leads not to electrostatically induced carriers but instead to the electric field-induced creation of oxygen vacancies, with consequent migration of oxygen from the oxide film into the ionic liquid. This mechanism should be taken into account in the interpretation of ionic liquid gating experiments.