  The phase diagram of a system constituted of neutrons, protons,
$\Lambda$-hyperons and electrons is evaluated in the mean-field approximation
in the complete three-dimensional space given by the baryon, lepton and strange
charge. It is shown that the phase diagram at sub-saturation densities is
strongly affected by the electromagnetic interaction, while it is almost
independent of the electric charge at supra-saturation density. As a
consequence, stellar matter under the condition of strangeness equilibrium is
expected to experience a first as well as a second-order strangeness-driven
phase transition at high density, while the liquid-gas phase transition is
expected to be quenched. An RPA calculation indicates that the presence of this
critical point might have sizable implications for the neutrino propagation in
core-collapse supernovae.
