RE: he was fired from the show and still under contract
So, his contract stipulates that he still be paid his salary even as he was fired from the show? Why would Fox do that?
So as effectively to stifle Carlson without (a) incurring liability by violating his employment contract, but, probably more importantly, without (b) facilitating his ability to pop up elsewhere and recommence conveying the same or a similar message.
Top keep him quiet.
If they fire him they will still have to pay him for the remainder of his contract.
So they might as well keep him to shut him up.