  The fermion mass spectrum is studied in the quenched approximation in the
strong coupling vortex phase (VXS) of a globally U(1)$_L \otimes$U(1)$_R$
symmetric scalar-fermion model in two dimensions. In this phase fermion
doublers can be completely removed from the physical spectrum by means of a
strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase
consists most probably only of a massive Dirac fermion which has charge zero
with respect to the $U(1)_L$ group. We give evidence that the fermion which is
charged with respect to that subgroup is absent in the VXS phase. When the
$U(1)_L$ gauge fields are turned on, the neutral fermion may couple chirally to
the massive vector boson state in the confinement phase. The outcome is very
similar to our findings in the strong coupling symmetric phase (PMS) of
fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the
exception that in four dimensions the neutral fermion does most probably
decouple from the bosonic bound states.
