The Villa chief executive also believes manager Remi Garde will stay with the club should they fall into the Sky Bet Championship.
Villa are eight points from safety ahead of Saturday's crunch clash at fellow strugglers Newcastle and have not won since the opening day.
They are on a club-record run of 15 winless league games and Fox insisted relegation will not lead to ruin.
He said: "We have taken significant steps to ensure we can cope financially.
"It is certainly not what we want and it is certainly not a lesson this club needs to learn to get better but Aston Villa is bigger than the results in any one season. Aston Villa does not go away if we are relegated.
"We play football next August and we hopefully do it with an organisation that is prepared to compete and to succeed and to come right back up. We're all in it together.
"We are building something special and Remi Garde is a massive part of what we are trying to build.
"I can't speak highly enough of his integrity and his willingness to come to our club knowing that what we are trying to do is a project.
"I have nothing but admiration for how he has handled himself since he came in and I am very confident we have a manager who will be with this club for a long, long time."
Villa are one of seven teams having never been relegated from the Premier League but look certain to go down having won just six points from 16 games.
No team in Premier League history has ever survived from that position but Fox has refused to give in.
He added: "I haven't given up, the manager hasn't given up and the players haven't given up. I certainly understand why people are frustrated. There is plenty of season left to play. In the more recent past people look at Leicester as a source of possibility and potential. This is an unusual league this year."
Fox and Garde met owner Randy Lerner in America this week and Garde admitted he was keen on Gent striker Laurent Depoitre.
He added: "He is a good player, he has had very good matches in the Champions League. Yes, I know him."