Bury face a 12-point deduction next season after owner Steve Dale put forward a proposal to help clear some of the club's debts.
In a company voluntary arrangement (CVA) proposal, seen by BBC Radio Manchester, Dale has offered to pay the club's football creditors in full.
Unsecured creditors, including HMRC, will be paid 25% of what they are owed.
If approved, the CVA would qualify as an insolvency event under EFL rules, which would see Bury deducted points.
The proposal states that football creditors are owed £950,652 while unsecured creditors are owed £5,982,765, including £3.6m to Dale.
The club appeared in the High Court last week over a winding-up petition originally brought by former head coach Chris Brass but which was taken over by HM Revenue & Customs (HMRC).
HMRC are now owed £1m but would be paid a quarter of what they are due under the arrangement, while Dale states he will not be seeking the money owed to him by the club.
The proposal requires agreement from creditors owed 75% or more of the total debts to be passed and also requires agreement from 50% of the club's shareholders.
The club are set to reappear in court on 9 July at 11:00 BST to meet with creditors and agree to a resolution.
Bury have experienced significant off-field problems over the past season and Dale says their troubles "turned out to be far in excess of what we could have comprehended" after he took over in December.
Club staff and players have experienced issues with delayed payment at the close of the 2018-19 season that saw them promoted back to League One.
What is a company voluntary arrangement?
An insolvent company can use a company voluntary arrangement to pay its creditors over a fixed period and, if they agree, the company can continue to trade.
The company needs to apply for its CVA through an insolvency practitioner who, within a month of their appointment, will work out an arrangement to cover how much of the debt it can pay as well as a payment schedule.
The creditors will then be invited to vote on the arrangement, however, the proposal must be approved by creditors who are owed at least 75% of the debt.
If 75% of creditors cannot agree on the arrangement, the company could face voluntary liquidation.