re: How to Destroy the ACC

This made me go look. If this defaults to NC law, then Section 55A-14-01 states that dissolution requires approval by:

(1) By the board;
(2) By the members entitled to vote thereon, if any, by two-thirds of the votes cast or a majority of the votes entitled to be cast on the plan of dissolution, whichever is less; and
(3) In writing by any person or persons whose approval is required by a provision of the articles of incorporation authorized by G.S. 55A-10-30 for an amendment to the articles of incorporation or bylaws.

The ACC has a "board" per subsection (1) that is comprised of the 15 schools presidents and chancellors. LINK
The ACC Constitution has rules for a quorum for the Board on certain topics, but the ACC Constitution is silent on dissolution. LINK This could be the sticking point.
Assuming every member gets a vote, then 8/15 schools meets subsection (2).
Subsection (3) appears to be related to a third party approval, if spelled out in the articles of incorporation, which I don't think the ACC would have.

So it very well may be possible to blow everything up with 8/15 schools.