AUSTIN, Tex.  It was an unusual hearing. The subject at the center of it all, Cameron Todd Willingham, was not present. After being convicted of murdering his three children in a 1991 house fire, he was executed in 2004.

Members of Mr. Willingham’s family, working with lawyers who oppose the death penalty, had asked for the rare and controversial hearing, held here on Thursday, to investigate whether Mr. Willingham was wrongfully convicted. They argue that the proceeding, known as a court of inquiry, could restore Mr. Willingham’s reputation, a right guaranteed under Texas law, even to the dead.

But they also say that the hearing is more than symbolic  it could cast in a new light the Lone Star State’s record on executions. And more broadly, they argue, it is a cautionary tale about the power of flawed science to sway a courtroom, and a glaring injustice that could affect debates over the fairness of the death penalty.

That debate has been framed, in part, by a 2006 opinion written by Justice Antonin Scalia of the United States Supreme Court, in which he said that the dissent in a case had not cited “a single case  not one  in which it is clear that a person was executed for a crime he did not commit.”