The classical hybrid combustion theory is generalized to solid fuels that form a liquid layer on their burning surface. For several classes of liquefying fuels, the layer is hydrodynamically unstable leading to substantial droplet entrainment from the melt layer into the gas stream. The susceptibility of a given fuel to this shear driven instability increases with decreasing viscosity and surface tension of the melt layer. The entrainment mass transfer, which acts in addition to the conventional gasification mechanism, is not affected by the blocking phenomenon induced by blowing from the surface. For practical oxidizer flux levels encountered in hybrid rocket applications, droplet entrainment can dominate direct gasification. Such liquefying fuels can exhibit greatly increased surface regression rates compared to classical materials such as HTPB. One application of the theory is to solid cryogenic hybrids, which utilize frozen materials for the solid propellant. The theory successfully predicts why high regression rates are observed in tests of cryogenic solid pentane, solid pentane and solid oxygen. In addition, the theory explains the dependence of the burning rates of other tested cryogenic materials on the physical properties of the liquid layer. The theory also leads to the conclusion that certain non-cryogenic materials such as paraffin and PE waxes will also exhibit high regression rates. This important result is confirmed by lab scale tests performed at Stanford University on a paraffin-based fuel.