  We investigate the possibility that mass transfer early in the evolution of a
massive binary can effect a reversal of the end states of the two components,
resulting in a neutron star which forms before a black hole. In this sense,
such systems would comprise the high-mass analogues of white dwarf-neutron star
systems such as PSR B2303+46. One consequence of this reversal is that a second
episode of mass transfer from the black hole progenitor star can recycle the
nascent neutron star, extending the life of the pulsar.
  An estimate of the formation rate through this channel is first performed via
a simple analytical approach, and then refined using the results of the SeBa
binary evolution package. The central role of kicks in determining the survival
rate of these binaries is clearly demonstrated. The final result is expressed
in terms of the number of field pulsars one can expect for every single neutron
star-black hole (ns,bh) binary. We also calculate this figure for black
hole-neutron star (bh,ns) systems formed through the usual channel. Assuming
kicks drawn from the distribution of Cordes & Chernoff (1998), we find an
expectation value of one (ns,bh) binary per 4 x 10^4 pulsars, and one (bh,ns)
system for every 1500 pulsars. This helps to explain why neither system has
been seen to date, though it suggests that detection of a (bh,ns) binary is
imminent.
