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In the past, SDSS J160429.12+100002.2 was spectroscopically classified as a blue horizontal branch (BHB) star. Assuming a luminosity that is characteristic of BHB stars, the object's radial velocity and proper motions from Gaia Early Data Release 3 would imply that its Galactic rest-frame velocity exceeds its local escape velocity. Consequently, the object would be considered a hypervelocity star, which would prove particularly interesting because its Galactic trajectory points in our direction. However, based on the spectroscopic analysis of follow-up observations, we show that the object is actually a short-period ($P \approx 3.4$ h) single-lined spectroscopic binary system with a visible B-type star (effective temperature $T_{\mathrm{eff}} = 15\,840\pm160$ K and surface gravity $\log(g) = 4.86\pm0.04$) that is less luminous than typical BHB stars. Accordingly, the distance of the system is lower than originally thought, which renders its Galactic orbit bound to the Galaxy. Nevertheless, it is still an extreme halo object on a highly retrograde orbit. The abundances of He, C, N, O, Ne, Mg, Al, Si, S, and Ca are subsolar by factors from 3 to more than 100, while Fe is enriched by a factor of about 6. This peculiar chemical composition pattern is most likely caused by atomic diffusion processes. Combining constraints from astrometry, orbital motion, photometry, and spectroscopy, we conclude that the visible component is an unevolved proto-helium white dwarf with a thin hydrogen envelope that was stripped by a substellar companion through common-envelope ejection. Its unique configuration renders the binary system an interesting test bed for stellar binary evolution in general and common-envelope evolution in particular.