In 2008, I reviewed and proposed a model for our discovery in 2005 that unrefoldable and insoluble proteins could in fact be solubilized in unsalted water. Since then, this discovery has offered us and other groups a powerful tool to characterize insoluble proteins, and we have further addressed several fundamental and disease-relevant issues associated with this discovery. Here I review these results, which are conceptualized into several novel scenarios. 1) Unlike 'misfolded proteins', which still retain the capacity to fold into well-defined structures but are misled to 'off-pathway' aggregation, unrefoldable and insoluble proteins completely lack this ability and will unavoidably aggregate in vivo with ~150 mM ions, thus designated as 'intrinsically insoluble proteins (IIPs)' here. IIPs may largely account for the 'wastefully synthesized' DRiPs identified in human cells. 2) The fact that IIPs including membrane proteins are all soluble in unsalted water, but get aggregated upon being exposed to ions, logically suggests that ions existing in the background play a central role in mediating protein aggregation, thus acting as 'dark mediators'. Our study with 14 salts confirms that IIPs lack the capacity to fold into any well-defined structures. We uncover that salts modulate protein dynamics and anions bind proteins with high selectivity and affinity, which is surprisingly masked by pre-existing ions. Accordingly, I modified my previous model. 3) Insoluble proteins interact with lipids to different degrees. Remarkably, an ALS-causing P56S mutation transforms the β-sandwich MSP domain into a helical integral membrane protein. Consequently, the number of membrane-interacting proteins might be much larger than currently recognized. To attack biological membranes may represent a common mechanism by which aggregated proteins initiate human diseases. 4) Our discovery also implies a solution to the 'chicken-and-egg paradox' for the origin of primitive membranes embedded with integral membrane proteins, if proteins originally emerged in unsalted prebiotic media.