FERRIDAY, La. — In the spring of 1965, the Federal Bureau of Investigation in Washington received a letter from Concordia Parish in northeastern Louisiana. Addressed to the bureau’s director, J. Edgar Hoover, the letter pleaded for justice in the killing of a well-respected black merchant.

A few months earlier, the businessman, Frank Morris, had come upon two white men early one morning at the front of his shoe-repair shop, one pointing a shotgun at him, the other holding a canister of gas. A match was ignited, a conflagration begun, and Morris died four days later of his burns without naming the men, perhaps fearing retribution against his family.

The letter expressed grave concern that the crime would go unpunished because the local police were probably complicit. “Your office is our only hope so don’t fail us,” it concluded. It was signed:

“Yours truly, The Colored People of Concordia Parish.”

Nearly five decades later, the Justice Department has written back — not directly to the family of Mr. Morris or to the black community of Concordia Parish, but to dozens of other families who lost loved ones during this country’s tumultuous and violent civil rights era....