Kree Flowers had recently gotten married and decided to log into her account on the Social Security Administration’s website in February to check on the status of her retirement benefits. She was shocked to see a big red number at the top of the page. According to the agency, she had been overpaid by $17,121.21.

“At that point, my mind immediately goes to fraud,” she said. “Someone collected benefits under my name — that’s what I was thinking.”

The next morning, when Ms. Flowers called the agency, a representative told her that she had been overpaid for benefits between 1995 and 2003 and was expected to repay the balance. This didn’t make sense to her: She was 10 years old when the disputed payments began. “My first instinct was to laugh and correct him,” she said.

But Ms. Flowers said the representative had seemed unfazed by her age and directed her to fill out a form to dispute the charges. A few days later, her sister realized that she had been overpaid by the same amount.

Every year for the past four years, the S.S.A. has sent out between $6 billion and $10 billion in overpayments for various benefit programs, according to federal disclosures. The agency has an uncollected overpayment balance of $23 billion as of October. This is a small fraction of the more than $1.4 trillion that the agency pays to about 71 million people each year.

A recent investigative report from KFF Health News and Cox Media found that while overpayments sometimes result from mistakes made by the agency or beneficiaries, “much of the fault lies within the system.” Benefit rules are hard to follow, the S.S.A. is understaffed, and there are frequently long lags between changes in beneficiaries’ income and adjustments to their benefits. These can all lead to overpayments that may go unnoticed for years.

Ms. Flowers, 38, called the agency dozens of times looking for answers. “No one could ever really tell us what happened,” she said. Earlier notices about the overpayment were sent to an old address, which was why Ms. Flowers had to discover it on her own. She suspects the issue stems from disability payments the agency made to her estranged father. (Social Security representatives told her that they were not allowed to disclose her father’s private information.)

In the 1990s, when her parents were separated and living in different states but still married, Ms. Flowers’s father applied for and received payments through the Social Security Disability Insurance program, which can cover recipients’ children. Her mother recalled receiving monthly payments of $100 or $120 for a year or so, but nowhere near $34,000 over eight years.

People who receive Social Security disability benefits are not allowed to earn more than $1,470 per month in additional income after a nine-month trial work period; beyond that threshold, their benefits are typically cut off. But there is often a lag between the time people become ineligible for benefits and the time their payments stop, either because they don’t realize they have to report a change in circumstances or because the administration is slow to process their case.

In an interview, Ms. Flowers’s father said that he believed he had been eligible for benefits during the overpayment period and that it was unclear to him what had happened. He said it was “outrageous” that the S.S.A. would seek to recoup money from people who were children when the payments were made.

The overpayment was not the fault of the Flowers siblings, and it may not have been their father’s fault, either. Yet the sisters were on the hook for it.

“I would say that work-related overpayments are the rule, not the exception,” said Denise Hoffman, principal researcher at Mathematica, a research and data analytics consultancy. Her research has found that while overpayments are rare in disability insurance overall, people whose earnings exceeded the threshold were overpaid about 80 percent of the time. Ms. Hoffman found that the median overpayment lasted nine months and totaled $9,282.

According to agency rules, dependents or spouses who are listed on the recipient’s records can be held liable for overpayments. People can also be held liable if they manage payments on behalf of another person, like an underage child or an older relative with dementia.

It’s not clear how frequently the agency tries to recoup overpayments from relatives of account holders. A spokesperson for the S.S.A. said that its system was not designed to easily determine this information, and that efforts were being made to clarify the issue. According to a 2016 report from the Government Accountability Office, about 30 percent of the people whose overpayments had been written off in the previous fiscal year were under 18 when their parents received benefits.

In 2015, when Sarah Benavidez’s daughter was 2 months old, Ms. Benavidez and the child’s father visited their local S.S.A. office to inquire about receiving benefits for the girl. They were told that their daughter was eligible for payments because her father, a former police officer, had been injured at work and qualified for disability insurance. Eventually, Ms. Benavidez received about $300 per month.

“It helped a lot, especially when she was in diapers,” she recalled.

The child’s father left soon after, Ms. Benavidez said, but she continued to receive checks for their daughter. In 2020, she received a letter from the S.S.A. that said the father had been receiving workers’ compensation payments while also receiving disability checks, resulting in an overpayment.

The parents had reported the workers’ compensation at the outset, but overpayments can still occur if “nobody at Social Security did the proper budgeting,” said Anne Callagy, director of the government benefits practice at the Legal Aid Society in New York. “And then years later, they get an overpayment notice.”

As a result, Ms. Benavidez’s 5-year-old daughter owed the Social Security Administration $12,768. “I was like, is this a scam?” Ms. Benavidez said.

The letter stated that she had 30 days to repay the money or else her daughter’s Social Security payments would stop. Ms. Benavidez asked for the charge to be reconsidered, but was unsuccessful. It wasn’t enough to show that the overpayment was not her fault — to win the appeal, she would also have to prove she could not repay the money, said Kathleen Romig, director of Social Security and disability policy at the Center on Budget and Policy Priorities.

“Almost no one completes the process successfully,” she said of overpayment waiver requests.

Ms. Benavidez’s daughter was still eligible to receive $120 per month, which the S.S.A. is withholding and crediting toward the overpayment balance. If nothing changes, her daughter’s overpayments will be considered repaid in 2030. More than 75 percent of recovered disability insurance overpayments are collected via withheld payments, according to the 2016 G.A.O. report.

“I just feel like they’ll take the money until they feel like they’ve paid off the thing,” Ms. Benavidez said. “I don’t even know if I want it back. I’m going to be paranoid.”

Recipients sometimes receive overpayment letters long after they’ve stopped getting benefits, and the S.S.A. tries to recoup the money in other ways.

Temi Aina, a resident of Queens, learned she was being charged for an overpayment when she didn’t receive an expected tax rebate. A few weeks later, a letter arrived from the S.S.A. saying she had received overpayments on her father’s account totaling $11,681 during four years that began in 2005, when she was 13. Her brother owed money, too.

She fought the case, providing evidence that showed her father had not used the money for her benefit. The case dragged on for two years. She lost two tax refunds totaling about $1,000, and at one point, she received a letter stating that the S.S.A. would begin garnishing her wages. But she had switched jobs by the time the agency contacted her former employer, so the change was not immediately effective.

Ms. Benavidez, Ms. Flowers and Ms. Aina all tried to fight their overpayment debt through the standard appeal process.

After Ms. Flowers submitted her appeal paperwork, she saw a TikTok video posted by someone in a similar situation. The person had contacted the local representative in Congress about the issue. Ms. Flowers, who lives in Norcross, Ga., reached out to Representative Lucy McBath, whose office contacted the S.S.A. Ms. Flowers appeared at a hearing this summer and was told that the financial information she had submitted proved she could not repay the money. Her $17,121 overpayment was taken off her account. Her sister’s case is continuing.

Ms. Flowers made a viral TikTok video about her experience and said she had heard from hundreds of people with similar stories.

Ms. Benavidez, who lives in Louisiana, saw Ms. Flowers’s video and tried to contact her House representative, Clay Higgins. She is hopeful she’ll get help resolving the overpayment. The S.S.A. continues to withhold her daughter’s $120 payments.

An agency representative said it worked with people to navigate the overpayment process. People have the right to appeal any overpayment or pursue a repayment plan with options as low as $10 per month.

Ms. Aina eventually connected with a lawyer at the Legal Aid Society who helped her. In July 2021, her remaining overpayment balance was waived.

Ms. Aina said she had cried tears of joy when she learned the remaining debt had been cleared. “I’m just really glad that it worked in my favor, because I feel like nobody should have to go through that if they’re not at fault,” she said. Her brother’s overpayment remains unresolved.