The biggest private legal settlement in the history of Wall Street was a few sentences away from death. In early June a little-known Texas lawyer named Kathy Patrick was putting the final touches on her carefully crafted $8.5 billion deal with Bank of America over so-called mortgage put-backs, when she got a last-minute demand from the other side. Sitting in her Houston office, Patrick learned that BofA wanted her clients—a clutch of the world’s most important investment firms, including...