  In the conventional approach, fermionic test fields lead to a generic
overspinning of black holes resulting in the formation of naked singularities.
The absorption of the fermionic test fields with arbitrarily low frequencies is
allowed for which the contribution to the angular momentum parameter of the
space-time diverges. Recently we have suggested a more subtle treatment of the
problem considering the fact that only the fraction of the test fields that is
absorbed by the black hole contributes to the space-time parameters. Here, we
re-consider the interaction of massless spin $(1/2)$ fields with Kerr and
Kerr-Newman black holes, adapting this new approach. We show that the drastic
divergence problem disappears when one incorporates the absorption
probabilities. Still, there exists a range of parameters for the test fields
that can lead to overspinning. We employ backreaction effects due to the
self-energy of the test fields which fixes the overspinning problem for fields
with relatively large amplitudes, and renders it non-generic for smaller
amplitudes. This non-generic overspinning appears likely to be fixed by
alternative semi-classical and quantum effects.
