  We analyze whether a black hole can exist and survive in a universe that goes
through a cosmological bounce. To this end, we investigate a central
inhomogeneity embedded in a bouncing cosmological background modeled by the
comoving generalized McVittie metric. Contrary to other dynamical metrics
available in the literature, this solution allows for the interaction of the
central object with the cosmological fluid. We show that the horizons
associated with this metric change with cosmic time because they are coupled to
the cosmic evolution as the mass of the central object is always proportional
to the scale factor: it decreases during contraction and increases during
expansion phases. After a full analysis of the causal structure of this
spacetime, we determine that a dynamical black hole persists during the
contraction, bounce, and expansion of the universe. This result implies that
there is a class of bouncing models that admits black holes at all cosmological
epochs. If these models are correct approximation to the real universe, then
black holes surviving a cosmic collapse could play some role in the subsequent
expanding phase.
