We present an ultraviolet color-magnitude diagram (CMD) spanning the hot horizontal branch (HB), blue straggler, and white dwarf populations of the globular cluster NGC 2808. These data were obtained with the far-UV and near-UV cameras on the Space Telescope Imaging Spectrograph (STIS). Although previous optical CMDs of NGC 2808 show a high-temperature gap within the hot HB population, no such gap is evident in our UV CMD. Instead, we find a population of hot subluminous HB stars, an anomaly only previously reported for the globular cluster ω Cen. Our theoretical modeling indicates that the location of these subluminous stars in the UV CMD, as well as the high-temperature gap along the HB in optical CMDs, can be explained if these stars underwent a late helium-core flash while descending the white dwarf cooling curve. We show that the convection zone produced by such a late helium flash will penetrate into the hydrogen envelope, thereby mixing hydrogen into the hot helium-burning interior, where it is rapidly consumed. This phenomenon is analogous to the "born again" scenario for producing hydrogen-deficient stars following a late helium-shell flash. The flash mixing of the envelope greatly enhances the envelope helium and carbon abundances, and leads, in turn, to a discontinuous increase in the HB effective temperatures at the transition between canonical and flash-mixed stars. We argue that the hot HB gap is associated with this theoretically predicted dichotomy in the HB properties. Moreover, the changes in the emergent spectral energy distribution caused by these abundance changes are primarily responsible for explaining the hot subluminous HB stars. Although further evidence is needed to confirm that a late helium-core flash can account for the subluminous HB stars and the hot HB gap, we demonstrate that an understanding of these stars requires the use of appropriate theoretical models for their evolution, atmospheres, and spectra.
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