Phil Neville has told Robbie Savage's Premier League Breakfast on BBC Radio 5 Live that his family are "devastated" about Bury's possible demise.
The club could be expelled from the English Football League on Friday unless owner Steve Dale can prove they have the funding to continue.
Neville said: "One man cannot stop one football club, which has hundreds of years of history, going out of existence.
"It's probably the biggest day in their history. Today Bury, the town, might not have a football club. It's absolutely disgraceful."
Bury-born Neville's mother Jill last week resigned as club secretary, while his late father Neville was a director.