The possibility that crystal-to-amorphous phase transformations can be induced by one or more underlying instabilities of the crystalline phase has been investigated in highly supersaturated solid solutions of Nb-Pd. Several unusual properties were discovered that may be identified as precursor effects of the collapse of the bcc α-Nb terminal solution to the amorphous phase. Elastic neutron diffraction measurements of α-Nb solutions found, with increasing Pd concentration, an anomalously large increase of the average atomic root-mean-square displacement to about half of the value at which the Lindemann criterion predicts the lattice should melt. Low-temperature heat capacity measurements yielded a concomitant decrease in the Debye temperature, suggesting that supersaturation causes an elastic modulus to soften. Single crystals of α-Nb solutions at high supersaturations have a highly anisotropic structure that is visible in transmission electron microscopy images; it is consistent with the development of a soft phonon mode leading to a bcc-to-ω phase transformation. Considered together with the results of other recent experiments, these findings suggest that shear instability of the crystalline phase plays an important role in the crystal-to-amorphous transformation and that the average static mean-square displacement of atoms in the lattice acts as a useful parameter for the stability of the crystal with respect to amorphization.