  The stability-limit conjecture (SLC) proposes that the liquid spinodal of
water returns to positive pressure in the supercooled region, and that the
apparent divergence of water's thermodynamic response functions as temperature
decreases are explained by the approach to this reentrant spinodal.
Subsequently, it has been argued that the predictions of the SLC are
inconsistent with general thermodynamic principles. Here we reconsider the
thermodynamic viability of the SLC by examining a model equation of state for
water first studied to clarify the relationship of the SLC to the proposed
liquid-liquid phase transition in supercooled water. By demonstrating that a
binodal may terminate on a spinodal at a point that is not a critical point, we
show that the SLC is thermodynamically permissible in a system that has both a
liquid-gas and a liquid-liquid phase transition. We also describe and clarify
other unusual thermodynamic behavior that may arise in such a system,
particularly that associated with the so-called "critical-point-free" scenario
for a liquid-liquid phase transition, which may apply to the case of liquid Si.
