  Though generally agreed that the symmetry energy plays a dramatic role in
determining the structure of neutron stars and the evolution of core-collapsing
supernovae, little is known in what concerns its value away from normal nuclear
matter density and, even more important, the correct definition of this
quantity in the case of unhomogeneous matter. Indeed, nuclear matter
traditionally addressed by mean-field models is uniform while clusters are
known to exist in the dilute baryonic matter which constitutes the main
component of compact objects outer shells. In the present work we investigate
the meaning of symmetry energy in the case of clusterized systems and the
sensitivity of the proto-neutron star composition and equation of state to the
effective interaction. To this aim an improved Nuclear Statistical Equilibrium
(NSE) model is developed, where the same effective interaction is consistently
used to determine the clusters and unbound particles energy functionals in the
self-consistent mean-field approximation. In the same framework, in-medium
modifications to the cluster energies due to the presence of the nuclear gas
are evaluated. We show that the excluded volume effect does not exhaust the
in-medium effects and an extra isospin and density dependent energy shift has
to be considered to consistently determine the composition of subsaturation
stellar matter. The symmetry energy of diluted matter is seen to depend on the
isovector properties of the effective interaction, but its behavior with
density and its quantitative value are strongly modified by clusterization.
