  General forms of the K\"ahler and superpotenials that lead to consistent low
energy broken Supersymmetry originating from $N=1$ Supergravity have been
classified and used for model building since more than three decades. We point
out the incompleteness of this classification when hidden sector vacuum
expectation values are of the order of the Planck mass. Focusing in this paper
mainly on the case of minimal K\"ahler potential, we adopt a rigorous approach
that retrieves on the one hand the known forms, and demonstrate on the other
hand the existence of a whole set of new forms for the superpotential of which
we give a complete classification. The latter forms involve a new type of
chiral superfields having the unusual property of belonging neither to the
hidden sector nor to the conventional observable sector. Comparing the obtained
forms with the conventional ones, we argue how new possibilities for model
building can arise, and discuss the gravity mediation of soft as well as
additional hard (but parametrically small) Supersymmetry breaking, in the
presence of the new type of chiral superfields. In the simplest case, we study
the vacuum structure, characterize the masses and couplings of the scalar
components to the hidden and observable sectors and discuss briefly the
physical role they could play. In the generic case, we estimate the magnitude
and possible consequences of the hard breaking of Supersymmetry in terms of the
interplay between hidden and visible sectors mass scales.
