They did (2007); back in the Championship now.
Last season Bradford City (a Premiership club briefly from 1999-2001) just missed becoming the first former Premiership club to go out of the Football League altogether, and Coventry City (in the first flight continuously from 1967-2001) are faced with a winding-up order from the revenuers, over unpaid stadium rent.
When they fall, they often fall hard.
Can a team be so bad that they get "relegated" out of the Football League? What happens to them after that? Do they become a "club" team? I'm curious about the inner workings of the British football leagues. Can I get that info online?