  We present an extensive study of accretion onto neutron stars in which the
velocity of the neutron star and structure of the surrounding medium is such
that the Bondi-Hoyle accretion exceeds .001 Msun/y. For most cases,
hypercritical accretion due to rapid neutrino cooling allows the neutron star
to accrete above the Bondi-Hoyle rate as previously pointed out by Chevalier.
However, for a subset of simulations which corresponds to evolutionarily common
events, convection driven by neutrino heating can lead to explosions by a
mechanism similar to that found in core-collapse supernovae.
  Armed with the results from our calculations, we are in a position to predict
the fate of a range of rapid-infall neutron star accretors present in certain
low-mass X-ray binaries, common envelope systems, supernova fallbacks and
Thorne-Zytkow objects (TZOs). A majority of the common envelope systems that we
considered led to explosions expelling the envelope, halting the neutron star's
inward spiral, and allowing the formation of close binary systems. Smothered
neutron stars produced in collisions also lead to explosions, preventing them
from forming millisecond pulsars. For supernovae in which the fallback of
material towards the neutron star is large, we find that a black hole is formed
within a few seconds. Finally, we argue that the current set of TZO formation
scenarios is inadequate and leads instead to hypercritical accretion and black
hole formation. Moreover, it appears that many of the current TZ models have
structures ill-suited for modeling by mixing length convection. This has
prompted us to develop a simple test to determine the viability of this
approximation for a variety of convective systems.
