  Roche lobe overflow from a donor star onto a black hole or neutron star
binary companion can evolve to a phase of unstable runaway mass-transfer,
lasting as short as hundreds of orbits ($\lesssim 10^{2}$ yr for a giant
donor), and eventually culminating in a common envelope event. The highly
super-Eddington accretion rates achieved during this brief phase ($\dot{M}
\gtrsim 10^{5}\dot{M}_{\rm Edd})$ are accompanied by intense mass-loss in disk
winds, analogous but even more extreme than ultra-luminous X-ray (ULX) sources
in the nearby universe. Also in analogy with observed ULX, this expanding
outflow will inflate an energetic `bubble' of plasma into the circumbinary
medium. Embedded within this bubble is a nebula of relativistic electrons
heated at the termination shock of the faster $v \gtrsim 0.1 c$ wind/jet from
the inner accretion flow. We present a time-dependent, one-zone model for the
synchrotron radio emission and other observable properties of such ULX
`hyper-nebulae'. If ULX jets are sources of repeating fast radio bursts (FRB),
as recently proposed, such hyper-nebulae could generate persistent radio
emission and contribute large and time-variable rotation measure to the bursts,
consistent with those seen from FRB 20121102 and FRB 190520B. ULX hyper-nebulae
can be discovered independent of an FRB association in radio surveys such as
VLASS, as off-nuclear point-sources whose fluxes can evolve significantly on
timescales as short as years, possibly presaging energetic transients from
common envelope mergers.
