As a part of the settlement, the N.F.L. agreed to make compensation payments that will stretch into the millions to retired players with severe cognitive and neurological problems. On paper, at least, the Websters should receive nearly $3 million based on his age at the time of the diagnosis, 50, and the number of years he played in the N.F.L., 17. The criteria are an attempt to gauge how long players were exposed to head trauma and how directly that exposure could be linked to health problems: Younger players are paid more on the presumption that football, not old age, caused their problems.

To the Websters’ dismay, they found out after the settlement agreement was announced that Iron Mike, as he was known in Pittsburgh, was not automatically part of it. That’s because the deal excludes players who died before Jan. 1, 2006.

The N.F.L. pushed for a cutoff date to prevent a stream of families from filing claims for long-deceased fathers and husbands. The plaintiffs’ lawyers ultimately agreed on 2006, which allowed more families to file claims, but was far enough back that it excluded the families of players who died before then from bringing wrongful-death and other suits against the league.

The Websters and other families in their position still have a glimmer of hope. The federal judge in the case, Anita B. Brody, left open a legal window for families of players who died before 2006 that their lawyers hope to utilize. Jason Luckasevic, the lawyer for the Websters, needs to show that the family still has the right to file a legal case against the league under their state’s statute of limitations.

Christopher Seeger, a co-lead counsel for the retired players who sued the league, declined to be interviewed on the phone. In an email, he explained that some players objected to the 2006 cutoff date, but without a settlement that at least captured players dating to 2006, many more would face the same stringent limitations as the Websters.