  We study the evolution of isolated self-interacting dark matter (SIDM) halos
that undergo gravothermal collapse and are driven deep into the
short-mean-free-path regime. We assume spherical Navarro-Frenk-White (NFW)
halos as initial conditions and allow for elastic dark matter
self-interactions. We discuss the structure of the halo core deep in the
core-collapsed regime and how it depends on the particle physics properties of
dark matter, in particular, the velocity dependence of the self-interaction
cross section. We find an approximate universality deep in this regime that
allows us to connect the evolution in the short- and long-mean-free-path
regimes, and approximately map the velocity-dependent self-interaction cross
sections to constant ones for the full gravothermal evolution. We provide a
semi-analytic prescription based on our numerical results for halo evolution
deep in the core-collapsed regime. Our results are essential for estimating the
masses of the black holes that are likely to be left in the core of SIDM halos.
