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We present the discovery of EVR-CB-004, a close binary with a remnant stellar core and an unseen white dwarf companion. The analysis in this work reveals the primary is potentially an inflated hot subdwarf (sdO) and more likely is a rarer post-blue horizontal branch (post-BHB) star. Post-BHBs are the short-lived shell-burning final stage of a blue horizontal star or hot subdwarf before transitioning to a WD. This object was discovered using Evryscope photometric data in a southern-all-sky hot subdwarf variability survey. The photometric light curve for EVR-CB-004 shows multi-component variability from ellipsoidal deformation of the primary and from Doppler boosting as well as gravitational limb darkening. EVR-CB-004 is one of just a handful of known systems, and has a long period (6.08426 hours) and large amplitude ellipsoidal modulation (16.0 $\%$ change in brightness from maximum to minimum) for these extremely close binary systems, while the properties of the primary make it a truly unique system. EVR-CB-004 also shows a peculiar low-amplitude (less than $1\%$) sinusoidal light curve variation with a period that is a 1/3 resonance of the binary period. We tentatively identify this additional variation source as a tidally-induced resonant pulsation, and we suggest followup observations that could verify this interpretation. From the evolutionary state of the system, its components, and its mass fraction, EVR-CB-004 is a strong merger candidate to form a single high-mass ($\approx1.2M_{\odot}$) WD. EVR-CB-004 offers a glimpse into a brief phase of a remnant core evolution and secondary variation, not seen before in a compact binary.