Completely backwards thinking. Even if those teams did leave, the Big 12 would be the one who raided the MWC not the other way around, since they have the Big TV contract already. Even if ESPN/ Fox negotiated them downwards, they would still make more than the AAC and MWC combined.
I've, obviously, never seen the TV contracts. But, if UT, Tech, OU, OSU and KU all left the B-XII, I'll guess that there are clauses that would prematurely terminate the agreements, as a loss of half of the (and all of the most valuable) parties. The absence of such contracts would negate any real viability of the conference.
The exodus would necessarily mean the expansion of, at least, one conference (presumably the SEC) to the magic number of "16." This would almost certainly mean continued expansion by the other power conferences. In such a scenario, it's hard to imagine a situation where WVU wouldn't be picked-up by another conference, if not the ACC, possibly, the SEC, itself.
With a core of just Baylor, ISU, KSU and TCU, the B-XII would cease to be a viable power conference. I suppose that the conference might be able to recruit twice the number of the then existing schools in order to survive under its name. But, this would likely mean nothing more than Mid-Major 2.0 + BYU and would be highly unlikely to assure continuation of the aforesaid TV contracts.
In the end, regardless of what you call it, the conference housing the remaining B-XII schools would be nothing more than the equivalent of the MWC (more likely) or the AAC. The semantics of branding would matter little. A B-XII with a Baylor, ISU, KSU and TCU core would be a non-power conference, regardless of name.