The mechanical rigidity or softness of metal-metal nanocontacts under large vibrations is important in nanoscale rheology and in technology. A puzzling shear-induced liquefaction under oscillatory strain, totally unexpected at room temperature, was suggested by recent experiments on nanosized gold junctions. Here we show theoretically that the simulated gold nanocontact structure actually remains crystalline even under large oscillatory strains. Tensile and compressive slips, respectively of “necking” and “bellying” types, do take place, but recover reversibly even during fast oscillatory cycles. We also explain why, counterintuitively, the residual stress remains tensile after both slips, driving the averaged stiffness from positive to negative, thus superficially mimicking a liquid’s. Unlike a liquid, however, the softening of the solid junction occurs by stick-slip, predicting largely frequency independent stiffness with violent noise in stress and conductance, all properties compatible with experiments. This surprising large amplitude rheology of nanojunctions and its consequences are likely to apply, with different parameters, to many other metals.