Caveats: I don't know much about academic requirements for the Big 12 (which are presumably minimal) or about non-football sports (except that Kansas has a good basketball team). That being said, here's two scenarios:
1. The standard story occurs: Nebraska to Big Ten, Colorado, Texas, Texas A&M, Texas Tech, Oklahama, Oklahoma State to Pac Ten.
Missouri, Iowa State, Baylor, Kansas, Kansas State remain.
Given that the Big Twelve would still be an autoqualifying BCS conference with five teams that have played together, why don't they pick off some of the top Mountain West teams? The Big Ten is to the Big Twelve what the Big Twelve is to the Mountain West, except that the value of the Big Twelve comes from the BCS payouts. Utah, TCU, and BYU could sidestep the whole autoqualifier issue by just joining a BCS conference, which would then have eight teams and be represented in Utah, Iowa, MIssouri, Kansas, and most importantly Texas.
The major hangup with the Mountain West has been that it's extremely top-heavy, while the bottom-feeders are very weak. Well, even a crappy BCS school that goes 4-8 is probably going 3-1 OOC a lot of years by feeding on the weak non-BCS teams; it would greatly improve the strength of the conference that contains Utah, TCU, and BYU and they wouldn't be fighting an uphill battle outside of the system.
Add in Boise State or some other schools for bonus points. Yeah, the $ are lacking, but it would be worse in C-USA, where a lot of those schools could be headed if the Big 12 falls apart. At this point, it would strictly be a matter of better than, and those schools would be better off than they would be otherwise unless the MWC is sure to become a BCS conference and snipes several of the old Big 12 schools. The latter part is sure, but the former part is not certain.
I mainly bring up this scenario to set up my optimistic, biased scenario 2.
2.Nebraska, Texas, Texas A&M to Big Ten; Colorado and Utah to Pac Ten.
Oklahoma, Oklahoma State, Texas Tech, Missouri, Iowa State, Baylor, Kansas, Kansas State remain.
If the Texas legislature likes Baylor so much, why would they allow it to be abandoned to perceived non-BCS doom? An eight team Big Twelve could turn into a southwest conference (ironically without Texas or Texas A&M), or it could expand if desired with some MWC teams, which would be less appealing without Utah. Either way, it would be an auto-qualifying conference, probably under the same name. The key here is that all four Texas teams would be in BCS conferences, while in the perceived PAC-16 scenario, Baylor would be left out.
This rests on the assumption that the Pac-10 doesn't really want to go to 16 without Texas - which is probably true. They need that brand name to justify watering down their existing, successful conference. The Pac-10 could go for Oklahoma, Oklahoma State... and then who? The Texas presence would be nice, but Tech and Baylor are pretty weak additions, and TCU is still just a small school. Do they try to illogically devour Kansas, or would they rather just go to 12 and call it quits?
Overall, I don't see why the Big Twelve has to die, if the schools causing instability (Texas and Nebraska) take off to the Big Ten. With a fourteen team Big Ten and a twelve team Pac Ten, there's nowhere left to run, and there's no real incentive to leave a BCS conference if there are no openings available elsewhere.
Also, in my hypothetical scenario 2, we give Notre Dame the finger and they stay independent.