That is, they aren't using him to do anything but still paying him per his contract.
Usually the contract would have a smaller amount of money they would have to pay him if he were not on the air. We do not know how much less Fox has to pay Carlson, but it is usually dependent on how arrogant the talent is. Very arrogant talent assumes that their employer would never want them off the air, and would not care if it were $1 a year. Tucker is very arrogant.