This letter reports a temperature-dependent limit for the subthreshold swing in MOSFETs that deviates from the Boltzmann limit at deep-cryogenic temperatures. Below a critical temperature, the derived limit saturates to a value that is independent of temperature and proportional to the characteristic decay of a band tail. The proposed expression tends to the Boltzmann limit when the decay of the band tail tends to zero. Since the saturation is universally observed in different types of MOSFETs (regardless of dimension or semiconductor material), this suggests that an intrinsic mechanism is responsible for the band tail.