Negative ions are not accurately represented in density functional approximations (DFAs) such as (semi)local density functionals (LDA or GGA or meta-GGA). This is caused by the much too high orbital energies (not negative enough) with these DFAs compared to the exact Kohn-Sham values. Negative ions very often have positive DFA HOMO energies, hence they are unstable. These problems do not occur with the exact Kohn-Sham potential, the anion HOMO energy then being equal to minus the electron affinity. It is therefore desirable to develop sufficiently accurate approximations to the exact Kohn-Sham potential. There are further beneficial effects on the orbital shapes and the density of using a good approximation to the exact KS potential. Notably the unoccupied orbitals are not unduly diffuse, as they are in the Hartree-Fock model, with hybrid functionals, and even with (semi)local density functional approximations (LDFAs). We show that the recently developed B-GLLB-VWN approximation [Gritsenko et al. J. Chem. Phys. 2016, 144, 204114] to the exact KS potential affords stable negative ions with HOMO orbital energy close to minus the electron affinity.