  We investigate the properties of the event horizon in the merger between a
large black hole and a smaller neutron star. We find that, if the star is
compact enough, then, in its rest frame a horizon begins to grow inside the
star before it merges with the black hole, in a manner analogous to the growth
of the event horizon in stellar collapse. We may say that, ahead of its fall
into the larger black hole, the neutron star begins to become a black hole
itself. We discuss how the phenomenon, even if not directly observable, can be
invariantly characterized. We demonstrate it quantitatively by explicitly
constructing the merger event horizon in the extreme-mass-ratio limit. We show
that the effect is present for realistic neutron star models and admissible
values of the compactness.
