  We study fermionic modes localized on the static spherically symmetric
self-gravitating non-Abelian monopole in the $SU(2)$
Einstein-Dirac-Yang-Mills-Higgs theory. We consider dependence of the spectral
flow on the effective gravitational coupling constant and show that, in the
limiting case of transition to the Reissner-Nordstr\"{o}m black hole, the
fermion modes are fully absorbed into the interior of the black hole.
