What do they do with a football club when it dies?
Talking from experience when my local club Hereford United died late in 2014, the record of games played that season was expunged, meaning any points gained by other teams against Hereford were lost, and every week one team didn't have a game to play.
Then a few individuals worked in conjunction with the Hereford United Supporters Trust (HUST) to set the wheels in motion to form a new club. for the following season, 2015/16. Prior to this, in the summer of 2014 Hereford had been kicked out of the National League Premier and had to drop two divisions to the Southern League Premier, due to not being able to satisfy the National League board that they had the necessary finance in place to complete the season. Because Hereford were in the Southern League Premier (tier 7 of the football pyramid) when going bust, the reformed club had to drop even further, to the Midland Premier, tier 9 of the pyramid. This is because the FA have a rule that all reformed clubs have to start at least 2 levels below where they were when they went bang. Effectively Hereford got relegated 4 divisions in little over a year.
The huge support for that level meant that Hereford were far greater than all the clubs at their new level, and achieved 3 promotions in three years, before eventually levelling out in the National League North (level 6). A lot of fans believe they have a divine right to go up again, but this is a really competitive league and I can't see Hereford getting out of it for some time, but at least there's still a club playing in the same stadium, in the same colours, with nearly the same name (the new club doesn't have "United" in its name).
I hope that Bury can do something similar, but my mate who is a Bury fan has fears that a phoenix club might not even be able to play in the town of Bury. Their stadium is currently owned by a company that does bridging loans, and the stadium is on prime development land. If the club goes bust, there's a possibility that it'll get sold off to a developer, rather than kept as a football stadium. Their supporters trust is in negotiations with this company, and apparently talks have gone ok, but I feel he's probably stringing them along.
If they can't get their stadium back then they'd have to groundshare with a smaller club in a neighbouring town, but that would likely see support drop off, and that's usually the difference that helps these clubs climb up through the lower leagues. They could end up doing a Scarborough, who played in Bridlington for 10 years, and never saw the kind of progress usually enjoyed by phoenix clubs.
I think their best bet is that somehow they're saved and somebody turns their fortunes around, but it's looking very very unlikely now