The Northwich Guardian says appendix E, the grounds on which the Conference demoted both clubs, is as follows:
A Club will not be eligible for membership of the Competition for the following season if by the second Saturday in May in the current season it shall be subject to an Insolvency Event.
Similarly, a Club shall not be eligible for membership of the Competition for the following season if between the second Saturday in May and the Annual General Meeting of the Company it has undergone an Insolvency Event.
Further, a Club will not be eligible for membership of the Competition for the following season if it shall have entered into an Insolvency Event during the preceding season and have exited such Insolvency Event without paying its creditors (including but not limited to football creditors) in full.
In the event of a Club suffering an Insolvency Event after the Annual General Meeting of the Company and prior to the start of the new season then the Club will cease to be eligible for membership of the Competition for the new season and the Club will be relegated from the Competition to a level within the National League System as may be decided upon by the Football Association.
Source:
http://www.northwichguardian.co.uk/vics/4423534.Conference_rules__Appendix_E_in_full/Looking at the second paragraph, I'd think Northwich's transgression is about as blatant as you can get. We were presumably demoted on the grounds of the first paragraph, but at least with us you could claim there's some ambiguity - arguing that we were still in rather than subject to an insolvency event by the second Saturday in May, the only event to affect it in that time was coming out of the thing.