– 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 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.

Several years ago, the FBI began reopening cold cases from that era — 112 at last count — raising hopes among some for justice. In all but about 20, though, the families of the long-dead have received letters, often hand-delivered by FBI agents, that say their cases have been closed, there is nothing more to be done — and please accept our condolences.

Simultaneously intimate and bureaucratic, these letters serve as epistolary echoes of an increasingly distant time. To some, they reflect the elusiveness of resolution in cases decades old; to others, they represent another missed opportunity for a full accounting of what ­happened, and why.

Grace Hall Miller, 80, a retired school board member in Newton, Ga., received one of these letters two years ago. It recounted a day in March 1965 that she hardly could have forgotten, when a man named Cal Hall Jr. fatally shot her husband, Hosie Miller, a farmer and church deacon, in a dispute over cows. Hall, who was white, shot Miller, who was black, in the back.

The letter recalled the notorious travel of the case, from repeated failures by grand juries to indict Hall to a “disproportionately white” jury’s finding against the Miller family in a wrongful-death lawsuit. It also summed up what the FBI had done after reopening the case: interviews with Miller and a family friend, a check with the local sheriff’s office and a search of county death records.

“After careful review of this incident, we have concluded that the now deceased Cal Hall Jr. acted alone when he shot and killed your husband, and therefore, we have no choice but to close our investigation,” the letter said. “We regret that we cannot be of ­further assistance to you. Again, please accept our sincere condolences for the loss of your husband” — a man who had died nearly a half-century earlier.

“It’s very unsatisfying,” said Shirley Sherrod, one of Miller’s six children. “Even after all these years, the system wouldn’t do anything. We didn’t get justice.”

Adam S. Lee, the chief of the FBI section overseeing civil rights, said that the bureau had been rigorous in pursuing these cold cases, following any evidence that might lead to prosecutions. But, he added, “That doesn’t bring the emotional closure that the public wants, or needs, in cases like this.”

In 2006, the FBI began a cold-case initiative that it described as a comprehensive effort to investigate racially motivated murders from the civil rights era. That effort became a mandate two years later when Congress passed the Emmett Till Unsolved Civil Rights Crime Act, named after the 14-year-old black boy who was tortured and killed in Mississippi in 1955, for supposedly flirting with a white woman.

From the outset, the government cited the formidable challenges it faced: the limited federal jurisdiction in some cases, the statute of limitations in others and, of course, time’s ­passage. Suspects and witnesses die. Evidence is lost. Memories dull.

Champions of the cold-case initiative debated its primary purpose. Was it justice, which would mean chasing those few cases with the highest likelihood of prosecution? Or was it truth, which would mean pursuing the facts in scores of cases, no matter that the ­principal players might be dead?

“Truth was the more realistic goal,” said Alvin Sykes, a human rights worker and an early champion of what became the Till Act, who envisioned a broad, aggressive effort to identify and investigate old civil rights cases. But he lowered his expectations, he said, once the narrower scope of the initiative became clear.

The law authorized tens of millions of dollars for the project, but so far only $2.8 million has come through.

Families who held out hope for prosecution have been disappointed. In a report to Congress in October, the Justice Department acknowledged the low yield from what it always considered to be long-shot efforts to develop cases worthy of prosecution.

The report said the FBI’s cold-case initiative had resulted in one successful federal prosecution, of James Ford Seale, who was convicted in 2007 in the deaths of two young black men in 1964. It also said the FBI had assisted in the 2010 state prosecution of a former Alabama trooper, James Bonard Fowler, in the shooting death of Jimmie Lee Jackson, a 26-year-old civil rights marcher who died after a confrontation with the police in 1965.

Left unsaid in the report was that these prosecutions were prompted in large part by the work of investigative journalists including Jerry Mitchell of the Clarion-Ledger in Jackson, Miss., John Fleming of the Anniston Star in Alabama, and David Ridgen, a Canadian documentary filmmaker.

As difficult as it might be to receive a letter saying that the investigation into your loved one’s death is being closed without a satisfying conclusion, there is the different pain of having no resolution at all, as in the 20 or so cold cases that remain open.

“Why they open it and why they open up wounds, I don’t know,” said Debra Sylvester, a daughter of Wharlest Jackson, whose pickup truck was blown up in 1967 after he accepted a promotion into a supervisory — that is, white — position at a tire plant. “My mama always said all you can do is pray. One day they’re going to have to give an account. One day they’re going to have to give an account to their maker.”