I'm as anti U of U sports as most, but bear with me. I'm somewhat optimistic about the future of BYU sports, maybe cautiously so, but still optimistic. But let's say the worst were to happen and either BYU got rid of Football/B-ball or simply continued to decline to the point of irrelevance. I think, hypothetically, one of the best things that could happen (and maybe poetic justice) would be for all of the die-hard and straight laced Mormon BYU supporters to switch allegiance to the U of U and claim it as their own. Play up the angle of Brigham Young having founded it, claiming it as the Mormon school, heavily publicizing and claiming it as such.
It would just be interesting to me what would happen in that hypothetical scenario to all the anti-Mormon and anti-BYU Utah fans. Would they bail? Would be fun to watch how it played out. Might also be fun to see how the Pac-12 leadership might squirm under that scenario.