The English Football League has agreed to discuss the option for the reinstatement of Bury into League Two in the future with its current members, as the fallout from the Shakers' demise continues.
After a number of attempts to instigate a takeover were ultimately unsuccessful, Bury were expelled from the EFL on 27 August, becoming the first club to be kicked out of the league system since 1992.
An eleventh-hour takeover attempt by the C&N Sporting Risk group didn't materialise, leaving the historic club teetering on the brink.

However, while Greater Manchester Police investigate allegations of fraud involving the club, a number of voices - including Bury North MP James Frith - have called for the club to re-enter the fourth tier for next season (2020/21).
As reported by the BBC, the EFL have shown a willingness to at least discuss the options for Bury being allowed a pathway to reinstatement into League Two. However, in a statement, the EFL also admitted that there is currently no set procedure in place to allow this to happen.
Part of the organisation's statement reads:

But the possibility of an application to the Football Association, which will determine the division Bury will play in, is already being discussed as MP Frith and Mayor of Manchester Andy Burnham target submission by 20 September.
But again, despite their early cooperation, the EFL reiterated that there is:
Greater Manchester Police says it is investigating a report of fraud involving Bury Football Club
— Sky News Breaking (@SkyNewsBreak) September 3, 2019