These judges fell behind when Gerald Ford was president. And they never caught up. Along the way, their office has become a bureaucratic parable — about what happens when the machinery of government cannot keep up with its good intentions.

In this case, the system became, in effect, too big to fix: Reforms were hugely expensive and so logistically complicated that they often stalled, unfinished. What’s left now is an office that costs taxpayers billions and still forces applicants to wait more than a year — often, without a paycheck — before delivering an answer about their benefits.

The experience of fighting this backlog can feel desperate and futile to people on both sides of the judge’s bench.

“I had two claimants on my docket this past month. . . . They died. They died. Waiting for a hearing,” said Carol Pennock, a Social Security judge based in Miami.

She worried that the two women might have improved if they’d lived long enough to be awarded disability benefits. In an especially absurd twist, even death didn’t remove one of those women from Social Security’s backlog. The woman had a child who might receive the woman’s disability benefits post-mortem. So Pennock said she had to hold a hearing to decide if a dead person was legally disabled.

“I really wonder if what we’re doing is effective at all. If it helps at all,” Pennock said, after a day of hearing cases and trying to reduce her share of the backlog. “If, based on the amount of evidence we get, my decision is any better than flipping a coin.”

A list of ailments

“She suffers from coronary artery disease, as well as depression, schizophrenia, migraines,” said the lawyer, a man with close-cropped hair whose firm advertises for frustrated Social Security applicants on the Internet. Also, he said, “she suffered an injury at work,” falling in a way that hurt her side.

In a small, spartan courtroom in Miami, this lawyer was laying out the maladies of a 52-year-old woman, who sat beside him in a gray zip-up sweatshirt. He was not done.

The woman also had a torn shoulder tendon, he said. And back pain. “Rules out any work,” the lawyer said, summing up the effect of these conditions.

The woman, a former Transportation Security Administration screener, had applied for disability benefits two years ago. She was scraping by without a paycheck, living with her mother and taking money from her brothers. And waiting. Now, at last, she would see a judge.

“Financially, I’m very stressed out,” the woman said outside the courtroom. Normally, Social Security hearings like this one are closed to the public. But the woman allowed a reporter to attend hers on the condition that her name not be used. “I can’t do anything at all,” she said. “I rely on too many people.”

The judge for her case was Timothy Maher, a lawyer who had been on the bench for six years. This was his second case of the afternoon. The first had been a burned-out cocaine addict who rambled incoherently. His case remains undecided.

Now, an hour later, Maher was on to a new person’s constellation of troubles. The woman’s attorney had listed seven different ailments — any one of which might render her legally disabled. Maher started with the coronary artery disease.