In January 2011, Joe Paterno learned prosecutors were investigating his longtime assistant coach Jerry Sandusky for sexually assaulting young boys. Soon, Mr. Paterno had testified before a grand jury, and the rough outlines of what would become a giant scandal had been published in a local newspaper.

That same month, Mr. Paterno, the football coach at Penn State, began negotiating with his superiors to amend his contract, with the timing something of a surprise because the contract was not set to expire until the end of the 2011 season, according to university documents and people with knowledge of the discussions. By August, Mr. Paterno and the university’s president, both of whom were by then embroiled in the Sandusky investigation, had reached an agreement.

Mr. Paterno was to be paid $3 million at the end of the 2011 season if he agreed it would be his last. Interest-free loans totaling $350,000 that the university had made to Mr. Paterno over the years would be forgiven as part of the retirement package. He would also have the use of the university’s private plane and a luxury box at Beaver Stadium for him and his family to use over the next 25 years.

The university’s full board of trustees was kept in the dark about the arrangement until November, when Mr. Sandusky was arrested and the contract arrangements, along with so much else at Penn State, were upended. Mr. Paterno was fired, two of the university’s top officials were indicted in connection with the scandal, and the trustees, who held Mr. Paterno’s financial fate in their hands, came under verbal assault from the coach’s angry supporters.