According to the telegraph the prem doesn't have the power to relegate a team (unless through points deduction), it does have the power to expel them from the league. But if it does so, the efl have no obligation to accept them (not sure if they could as it would be an extra team). So if they are expelled city would have to find a league to play in.
Edit - the prem would have to take an extra team from the efl to make up the shortfall. Unless they wanted to drop the league to 19 teams which might be a thing with extra games in the european competitions.
Edit - the prem would have to take an extra team from the efl to make up the shortfall. Unless they wanted to drop the league to 19 teams which might be a thing with extra games in the european competitions.