When I was in San Diego in the 90's, KFMB FM which was Hot AC, had a weeknight talk show hosted by Dr. Theresa L. Crenshaw, who would give love and dating advice. They played no music during that show, so it was all talk. The competing station, Q106 ran a similar show. Where I live now, the classic rock station plays Bob and Tom, and there's no music on that. These are just a few examples, but there are many others. So it's not that unsual, especially since WXLO is only doing it on Sunday nights, which is probably among the lowest rated periods.
Also, do you know if this is a brokered time show (paid slot)?