Barium.Sulfate.Ksp=1.5x10−9 => Solubility=√Ksp = √1.5x10−9 = 3.9x10−5M. This means that there is very little chance Na+ will react with SO2−4ion and very little chance that the GpIIA Ba+2 will react with the Cl−. ion. Simply, there is no driving force for formation of product with Barium Sulfate + Sodium Chloride as reactants in the problem.
Theoretically, BaSO4+2NaCl⇒Na2SO4+BaCl2 but neither sodium sulfate or barium chloride would form an insoluble precipitate (required) to be the driving force. Therefore, no reaction occurs.