  We address the question concerning the maximum density, at which nuclei (and
more generally -- nuclear structures) can exist in neutron star interiors. An
absolute upper bound to such a density is obtained using the bulk
approximation, in which surface and Coulomb effects are neglected. A very good
approximation to the limiting density is given by the threshold for the
instability of a uniform n-p-e plasma with respect to density modulations; this
threshold is calculated using the Extended Thomas-Fermi approximation for the
Skyrme energy functionals. For recent SLy Skyrme forces, which are particularly
suitable for the description of very neutron rich nucleon systems, the maximum
density at which nuclear structures can exist is 0.08 nucleons/fm^3 (i.e., half
of the normal nuclear density); at this density protons constitute only 4\% of
nucleons.
