Experimental investigation of cavitation in liquid helium 3 has revealed a singular behaviour in the degenerate region at low temperature. As the temperature decreases below 80 mK, the cavitation pressure becomes significantly more negative. To investigate this, we have extrapolated the Fermi parameters in the negative pressure region. This allowed us to calculate the zero sound velocity, which we found to remain finite at the spinodal limit where the first sound velocity vanishes. We discuss the impact on the nucleation of the gas phase in terms of a quantum stiffness of the Fermi liquid. As a result we predict a cavitation pressure which is nearer to the spinodal line than previously thought.