Phase separation in gets swollen by nematic solvents is investigated using a time-dependent Ginzburg-Landau model. We demonstrate that elasticity of the polymer network is responsible for a foam-like domain morphology observed in polymer dispersed liquid crystals (PDLCs). Rubber elasticity also prevents domain merger, leading to a coarsening behavior substantially slower than in liquid-liquid demixing. We briefly discuss phase separation in nematic polymer gets, in which operates a novel anchoring mechanism mediated by elastic strain.