Chemistry question about electron affinity

I see that many of the elements have a negative energy requirement for adding a valence electron, i.e., energy is given off by the action. From this I infer that adding the electron should be rather easy, yet I have never heard of a sodium or potassium ion with a negative charge (as it would have with an extra electron.)

If I am correct that Na- and K- do not exist, why is this so? The affinity energy implies that there would be some stability for such ions.