Both clubs have until 17:00 BST on Monday to show they can meet "all outstanding commitments".
Bolton have been in administration since 13 May, with a protracted takeover still not complete.
Bury, meanwhile, need to give details of how they plan to settle their debts after a company voluntary arrangement (CVA) was approved by creditors on 18 July.
Both will start the 2019-20 campaign with 12-point deductions resulting from their financial difficulties.
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