Analyzing the first equation in the BBGKY chain of equations for an equilibrium liquid-gas system, we derived the analytical expression for the atom work function from liquid into gas. The coupling between the atom work function from liquid into vacuum and the stability criterion of liquid in limiting points of the first type was shown (using I.Z. Fisher classification). As it turned out, Fisher's criterion corresponds to the condition of atomization. We have expressed the state equation in terms of the atom work function from liquid into vacuum and performed calculations of the limiting line of stability composed of limiting points of the first type for argon. Our model discovers an interesting effect of the negative atom work function: at a constant volume of liquid, on a temperature rise (also at a fixed temperature and decreasing specific volume of liquid) the atom work function drops and takes a negative value with a modulus that is significantly larger than the atomic thermal energy. We propose a new two-stage mechanism of sonoluminescence based on non-thermal processes in liquid in a state with a negative atom work function. The first stage includes the emission of atoms from the interior of the bubble into gas at hyper-thermal velocities. At the second stage, a collision of emitted flow takes place between the gas atoms along with the implosion of the central part of the bubble. As a result of the impact excitation, ionization and the subsequent recombination, a flash of electromagnetic radiation develops that can be seen in sonoluminescence experiments.