Can any liquid be cooled down below its melting point to an isentropic (Kauzmann) temperature without vitrifying or crystallizing? This long-standing question concerning the ultimate fate of supercooled liquids is one of the key problems in condensed matter physics and materials science. In this article, we used a plethora of thermodynamic and kinetic data and well established theoretical models to estimate the kinetic spinodal temperature, TKS (the temperature where the average time for the first critical crystalline nucleus to appear becomes equal to the average relaxation time of a supercooled liquid), and the Kauzmann temperature, TK, for two substances. We focused our attention on selected compositions of the two most important oxide glass-forming systems: a borate and a silicate-which show measurable homogeneous crystal nucleation in laboratory time scales-as proxies of these families of glass-formers. For both materials, we found that the TKS are significantly higher than the predicted TK. Therefore, at ambient pressure, at deep supercoolings before approaching TK, crystallization wins the race over structural relaxation. Hence, the temperature of entropy catastrophe predicted by Kauzmann cannot be reached for the studied substances; it is averted by incipient crystal nucleation. Our finding that TKS > TK for two real glasses corroborate the results of computer simulations for a pressurized silica glass.