Soluble folded proteins maintain their structural integrity by properly shielding most backbone amides and carbonyls from full hydration. This structure "wrapping" entails a proper packing of the intramolecular hydrogen bonds. Thus, a poorly wrapped hydrogen bond constitutes an identifiable packing defect. Such defects are promoters of protein associations since they favor the removal of hydrating molecules. In this work we show that large clusters of packing defects generate the most significant dehydration hot spots on the protein surface, inducing a strong dielectric modulation that is reflected by a local quenching of the dielectric permittivity. The PDB-reported proteins with the largest clusters of packing defects are found to be three cancer-related transcription factors, four highly interactive proteins related to cell signaling and cytoskeleton, and a cellular prion protein. A large concentration of packing defects in a soluble protein constitutes a structural singularity that is intermediate between order and disorder. The functional implications of this singularity are investigated to delineate diverse interrelated roles. The presence of these large clusters signals a structural vulnerability, a pronounced dehydration propensity, and a strong electrostatic enhancement.