  For those deformations that satisfy a certain non-degeneracy condition, we
describe the structure of certain simple modules of the deformations of the
subcharacter algebra of a finite group. For finite abelian groups, we prove
that the deformation given by the inclusion of the natural numbers, which
corresponds to the algebra generated by the fibred bisets over a field of
characteristic zero, is not semisimple. In the cyclic group of prime order
case, we provide a complete description of the semisimple deformations.
