Indeed, solid nanoparticles can stabilize the emulsion. The mechanism of their action is similar to the mechanism of action of surfactants. If you add salt, its ions are adsorbed on solid nanoparticles and the emulsion collapses. If you add surfactant, the surfactant will displace solid nanoparticles from the surface of the emulsion. Depending on the nature of the surfactant, liquid and solid nanoparticles there will be competition that is difficult to predict. Experiment is needed.
If we speak about preparing the emulsions with aqueous phases with different salt content there will be numerous options depending on many factors. Important to note that there is not only one 'stability' - however, relative stabilization or lack of it against creaming/sedimentation, coalescence, agglomeration, Ostwald ripening and phase inversion.
A bit simpler case would be if a given emulsion is subjected to different environment. Particle stabilized emulsions have usually high coalescence stability, likely what might occur will be destabilization by agglomeration. Depending on case situation in presence of e.g. anionic surfactant presence of multivalent cations (e.g. Ca) may trigger surfactant adsorption onto negatively charged particle surfaces making them hydrophobic.