Dover chairman Jim Parmenter says the Whites will not pay the £40,000 fine imposed by the National League after the club stopped playing matches.
The club has also been docked 12 points for next season after putting almost all staff on furlough because of costs associated with the Covid-19 pandemic.
Dover refused to take on loans to cover the costs of playing, having started the season with government grant money.
"They know we've got no money," Parmenter told BBC Radio Kent.
"They know we've done this to prevent us becoming insolvent, and yet they've fined us £40,000 which in itself will push us into insolvency if they enact it.
"It was the National League that insisted or pushed the clubs to start the season with those grants on the basis that further grants would be forthcoming."
Some clubs are considering a vote of no confidence in the National League board after a number of sides in the National League's North and South divisions were fined for refusing to play matches - both leagues have since been declared null and void.
"Our club and other clubs started the season at the behest of the National League," said Parmenter.
"The National League then failed to deliver on their promise of further grants so the National League have got nobody else to blame but themselves.
"Football has got a problem with its governance, particularly below the Football League," he added.
"This will bring it to a head and there will be legal action on this because it's time somebody stood up and said 'this is not right'."
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