Yield stress fluids are widely used in industrial application to arrest dense solid particles, which can be studied by using a concentrated emulsion as a model fluid. We show in experiments that particle sedimentation in emulsions cannot be predicted by the classical criterion for spheres embedded in a yield stress fluid. Phase separation processes take place, where a liquid layer forms and particle sedimentation is enhanced by the emulsion drainage. In addition, emulsion drainage can be arrested or enhanced by the amount of particles embedded in the emulsion. A minimal mathematical model is developed and solved in numerical simulations to describe the emulsion drainage in the presence of particles, which favorably compares with the experimental stability diagram and the sedimentation dynamics.