Subsequent stages of atomic-deficient nanostructurization finalizing rare-earth functionality under Pr3+-doping in Ga2(As0.28Sb0.12Se0.60)98 glass are studied employing method of positron annihilation lifetime spectroscopy. Genesis of free-volume positron trapping sites, composed of atomic-accessible geometrical holes (void cores) arrested by surrounding atomic-inaccessible Se-based bond-free solid angles (void shells), are disclosed for parent As2Se3, Ga-codoped Ga2(As0.40Se0.60)98, as well as Ga-codoped and Sb-modified Ga2(As0.28Sb0.12Se0.60)98 glasses. The finalizing nanostructurization due to Pr3+-doping (500 wppm) in glassy Ga2(As0.28Sb0.12Se0.60)98 is explained in terms of competitive contribution of changed occupancy sites available for both rare-earth ions and positrons.