Solutions of proteins and other molecules exhibit puzzling, mesoscopically sized inclusions of a solute-rich liquid, well outside the region of stability of the solute-rich phase. This mesoscopic size is in conflict with existing views on heterophase fluctuations. Here we systematically work out a microscopic mechanism by which a metastable solute-rich phase can readily nucleate in a liquid solution. A requisite component of the mechanism is that the solute form long-lived complexes with itself or other molecules. After nucleated in this non-classical fashion, individual droplets grow until becoming mechanically unstable because of a concomitant drop in the internal pressure, the drop caused by the metastability of the solute-rich phase. The ensemble of the droplets is steady-state. In a freshly prepared solution, the ensemble is predicted to evolve in a way similar to the conventional Ostwald ripening, during which larger droplets grow at the expense of smaller droplets.