The cubic antifluorite structure comprises a fcc sublattice of anions with cations on the tetrahedral sites. The voids in the antifluorite structure that are crucial for superionicity in ${\mathrm{Li}}_{2}\mathrm{O}$ might also act as atomic traps. Trapping of guest atoms and small molecules within voids of a host structure leads to the formation of what are known as clathrate compounds. Here we investigate the possibility of trapping helium or larger neon guest atoms under pressure within alkali-metal oxide and sulfide structures. We find stable helium and neon-bearing compounds at very low pressures. These structures are stabilized by a reduction in volume from incorporation of helium or neon atoms within the antifluorite structure. We predict that ${\mathrm{NeCs}}_{2}\mathrm{S}$ could be stable at ambient pressure. Our study suggests a novel class of alkali oxide and sulfide materials incorporating noble-gas atoms that might potentially be useful for gas storage.