  We consider the phenomenological implications of a soft SUSY breaking term BN
at the TeV scale (here B is the U(1)_Y gaugino and N is the right-handed
neutrino field). In models with a massless (or nearly massless) neutralino,
such a term will give rise through the see-saw mechanism to new contributions
to the mass matrix of the light neutrinos.
  We treat the massless neutralino as an (almost) sterile neutrino and find
that its mass depends on the square of the soft SUSY breaking scale, with
interesting consequences for neutrino physics. We also show that, although it
requires fine-tuning, a massless neutralino in the MSSM or NMSSM is not
experimentally excluded. The implications of this scenario for neutrino physics
are discussed.

High Energy Physics - Phenomenology