Problems in chemical thermodynamics: Doubts regarding the calculation of component fugacities in liquid phase mixtures

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Dear experts, I recently read the sections on EOS calculations for vapor-liquid equilibrium in textbooks on chemical thermodynamics, and I have a question: typically, the textbooks state that the expressions for the fugacity coefficients of components in the vapor phase and the liquid phase are identical. However, when calculating the fugacity of components in a liquid mixture, it is necessary to replace the volume V in the fugacity coefficient expression with the molar volume of the liquid phase, and to replace the composition with the mole fractions of the components in the liquid phase. That’s generally how it is explained. But in reality, for the expression of the fugacity coefficient of components in the liquid phase, it involves integrating from a finite liquid phase volume Vt (the volume of the liquid phase at temperature T and pressure p) to an infinite volume (where temperature T and pressure p approach 0). My question is: does the liquid phase volume approach infinity as the pressure approaches 0? In fact, when the pressure tends to 0, there should be no liquid phase. Please ask the experts to help solve this, thank you!