  The ultimate fates of binary companions to stars (including whether the
companion survives and the final orbit of the binary) are of interest in light
of an increasing number of recently discovered, low-mass companions to white
dwarfs (WDs). In this Letter, we study the evolution of a two-body system
wherein the orbit adjusts due to structural changes in the primary, dissipation
of orbital energy via tides, and mass loss during the giant phases; previous
studies have not incorporated changes in the primary's spin. For companions
ranging from Jupiter's mass to ~0.3 Msun and primaries ranging from 1-3 Msun,
we determine the minimum initial semimajor axis required for the companion to
avoid engulfment by the primary during post-main-sequence evolution, and
highlight the implications for the ultimate survival of the known exoplanets.
We present regions in secondary mass and orbital period space where an engulfed
companion might be expected to survive the common envelope phase (CEP), and
compare with known M dwarf+WD short-period binaries. Finally, we note that
engulfed Earth-like planets cannot survive a CEP. Detection of a
first-generation terrestrial planet in the white dwarf habitable zone requires
scattering from a several-AU orbit to a high-eccentricity orbit (with a
periastron of ~Rsun) from which it is damped into a circular orbit via tidal
friction, possibly rendering it an uninhabitable, charred ember.
