Supernovae of Type Iax (SNe Iax) are an accepted faint subclass of hydrogen-free supernovae. Their origin, the nature of the progenitor systems, however, is an open question. Recent studies suggest that the weak deflagration explosion of a near-Chandrasekhar-mass white dwarf in a binary system with a helium-star donor could be the origin of SNe Iax. In this scenario, the helium-star donor is expected to survive the explosion. We use the one-dimensional stellar evolution codes MESA and Kepler to follow the postimpact evolution of the surviving helium companion stars. The stellar models are based on our previous hydrodynamical simulations of ejecta-donor interaction, and we explore the observational characteristics of these surviving helium companions. We find that the luminosities of the surviving helium companions increase significantly after the impact: they could vary from 2500 L (circle dot) to 16,000 L (circle dot) for a Kelvin-Helmholtz timescale of about 10(4) yr. After the star reaches thermal equilibrium, it evolves as an O-type hot subdwarf (sdO) star and continues its evolution along the evolutionary track of a normal sdO star with the same mass. Our results will help to identify the surviving helium companions of SNe Iax in future observations and to place new constraints on their progenitor models.