How does salt separate glycerin from soap during the boiling process?

During the traditional boiling process, salt is used to separate glycerin from soap through a technique known as "salting out." This process relies on the fundamental difference in solubility between the two substances when exposed to a brine solution.1

When brine is added to the pasty, emulsified mass of soap and glycerin, the soap becomes insoluble in the salt solution, causing it to separate and form a curdy, grainy mass that floats to the top of the kettle. Conversely, glycerin remains soluble in the aqueous salt solution. This mixture, which settles at the bottom of the kettle, is known as spent lye. Once the layers have separated, the spent lye is extracted from the bottom of the vessel, allowing for the subsequent recovery and purification of the glycerin.1