English Football League executive chairwoman Debbie Jevans says she wants clubs to consider salary caps.
It follows the grim financial struggles of Bolton and Bury.
While the sale of Sky Bet League One club Bolton to Football Ventures was completed on Wednesday, Bury had already seen a prospective takeover and last-minute rescue talks collapse, before losing their EFL status.
"We understand Phil Parkinson and Steve Parkin's decision to leave the club," Football Ventures said, in a statement.
"They have behaved impeccably and loyally, and we wish them both nothing but the best for whatever the future may hold.
"It is now imperative that we commence the process of appointing a manager and strengthening the team with the right players to take the club forward."
