I think his contract hasn't expired yet so they can't kick him out. Although he makes a lot of backhanded comments about Trump and his administration he has never crossed the line for him to be fired. It is obvious Fox is censoring him and there is a lot of stuff happening behind the scenes Funny how his feud with Kellyanne suddenly disappeared as if it didn't happen I also think it doesn't benefit Fox to fire Shep because it would make it blatantly obvious they are bias and not "fair and balanced." I am pretty sure Shep is hoping he would get a job at CNN.
BTW, there is a "feud" going on between Hannity and Shep. Hannity has been throwing shade. Interestingly, Shep responded by telling to Mediaite...and CNN : "Sometimes facts are displeasing. Journalists report them without fear or favor." And Hannity's response..."I'm not a journalist, I'm a talk show host."