In his 46th season as the Penn State head coach, Mr. Paterno, 84, has had an extraordinary run of success: one that produced tens of millions of dollars and two national football championships for the university and established him as a revered leader in sports, but one that will end with a stunning and humiliating final chapter.

Mr. Sandusky, a former defensive coordinator under Mr. Paterno, has been charged with sexually abusing eight boys across a 15-year period. After leaving the football program following the 1999 season, Mr. Sandusky worked with Second Mile, a foundation he established to help needy children.

Mr. Paterno has been widely criticized for failing to involve the police when he learned of the 2002 incident involving the young boy. Additionally, two top university officials — Gary Schultz, the senior vice president for finance and business, and Tim Curley, the athletic director — were charged with perjury and failure to report to the authorities what they knew of the allegations, as required by state law.

Since Mr. Sandusky’s arrest Saturday, officials at Penn State — notably its president, Graham B. Spanier, and Mr. Paterno — have come under withering criticism for a failure to act adequately after learning, at different points over the years, that Mr. Sandusky might have been abusing children. Newspapers have called for their resignations; prosecutors have suggested their inaction led to more children being harmed by Mr. Sandusky; and students and faculty at the university have expressed a mix of disgust and confusion, and a hope that much of what prosecutors have charged is not true.

Mr. Paterno has not been charged in the matter, but his failure to report to the authorities what he knew about the 2002 incident has become a flashpoint, stirring anger on the board and an outpouring of public criticism about his handling of the matter.

On Monday, law-enforcement officials said that Mr. Paterno had met his legal obligation in alerting his superiors at the university when he learned of the 2002 allegation against Mr. Sandusky. But they suggested he might well have failed a moral test for what to do when confronted with such a disturbing allegation involving a child not even in his teens. No one at the university alerted the police or pursued the matter to determine the well-being of the child involved. The identity of that child remains unknown, according to Linda Kelly, Pennsylvania’s attorney general.