Inspired by the recent discoveries of circumbinary planets orbiting nine close binary stars, we explore the fate of the former as the latter evolve off the main sequence. We combine binary star evolution models with dynamical simulations to study the orbital evolution of these planets as their hosts undergo common-envelope (CE) stages, losing in the process a tremendous amount of mass on dynamical timescales. Five of the systems experience at least one Roche-lobe overflow and CE stage (Kepler-1647 experiences three), and the binary stars either shrink to very short orbits or coalesce; two systems trigger a double-degenerate supernova explosion. ' circumbinary planets predominantly remain gravitationally bound at the end of the CE phase, migrate to larger orbits, and may gain significant eccentricity; their orbital expansion can be more than an order of magnitude and can occur over the course of a single planetary orbit. The orbits these planets can reach are qualitatively consistent with those of the currently known post-CE, eclipse-time variations circumbinary candidates. Our results also show that circumbinary planets can experience both modes of orbital expansion (adiabatic and nonadiabatic) if their host binaries undergo more than one CE stage; multiplanet circumbinary systems like Kepler-47 can experience both modes during the same CE stage. Additionally, unlike Mercury orbiting the Sun, a circumbinary planet with the same semimajor axis can survive the CE evolution of a close binary star with a total mass of 1 .
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