For the sake of argument, let's discuss this on the premise that nine votes for dissolution would be sufficient.
If you remember the gyrations the member schools went through when we first reconstituted the BE in 2004 (eight non-football members, eight football members), it was because a group of schools cannot join together, call themselves a conference and have the NCAA accept them as a conference. This was setup so that after eight years (I believe the agreement the schools signed when we added UL, UC, USF, DePaul and Marquette was aligned with NCAA recognition rules) the two factions could leave (we can get into the details later) the member schools could continue as separate valid conferences.
If any school votes for dissolution of the ACC, they would have to know that they have a home in an existing conference. The schools that voted to not dissolve would potentially have a claim for damages against the schools that left and the conferences that took them in. This wouldn't be the BE claiming the ACC was trying to destroy the conference, it would be schools that got left out in the cold (and lost tens of millions in annual revenues) bringing a suit because they did destroy a conference.