The investigators presented their conclusions in a damning report to the authorities in Malta last summer, according to interviews with people involved in the case and to records obtained by The New York Times. But nothing appears to have been done, underscoring what experts say is a major flaw in European Union governance: Even when Brussels suspects wrongdoing by officials, staff members often can do very little about it, because enforcement is largely up to the member nations.
It is an especially ripe issue as the European Union continues to face attacks from nationalists and populists, who portray officials serving in Brussels as arrogant and untouchable.
Carl Dolan, of the Brussels office of Transparency International, said the European Union’s anti-fraud office was “fighting corruption with one hand tied behind its back.”
He added: “Without proper policing powers or help from member states, it simply serves to tip off fraudsters that they are under suspicion so they can destroy any evidence when, or if, they are finally prosecuted.”
Giovanni Kessler, the head of the anti-fraud office, which prepared the scathing report on Mr. Dalli, acknowledges the problem. “When it comes to judicial cooperation, Europe is still fragmented along national borders,” he said in a speech last year.
Mr. Kessler and his staff would not discuss the report about Mr. Dalli, saying they were not permitted to do so.
Reached by phone and asked about the fraud investigation, Mr. Dalli said: “Listen, listen, listen. That case has been fomented by Kessler. A false report has been sent to the Malta police which has been investigated, O.K., and nothing has come out of it.” He then hung up.
His account was not supported by other officials, however.
The report from Mr. Kessler’s office was sent to the office of Malta’s attorney general, Peter Grech. In a statement, Mr. Grech said his office would refer such findings to the police if there were “the possibility of criminally sanctionable conduct,” but he declined to discuss the Dalli case.
A spokeswoman for the Maltese police, Louise Camilleri, said that “investigations are still ongoing.”
The F.B.I. says it has struggled to get information from Malta. “That’s what we’re looking for,” said Donald A. Wood, an agent in the Columbia, S.C., office, when asked about the fraud scheme.
Mr. Dalli, born into a family of modest means during the bleak postwar years in Malta, trained as an accountant before becoming a management consultant and politician.
Elected to Parliament in 1987, he became finance minister and then foreign minister. In 2010, he was sent to Brussels as the Maltese member of the European Commission, where each of the European Union’s now 28 members is represented.
Soft-spoken and unassuming, Mr. Dalli nonetheless managed to court controversy almost as soon as he arrived as commissioner for health and food safety, by approving the planting of a genetically modified potato in Europe, riling environmentalists.
His other major focus was tobacco regulation. He championed a law forcing cigarette makers to include health warnings that cover most of the surface of their boxes.
Mr. Dalli was forced to step down when it emerged that a Maltese acquaintance had sought 60 million euros from a Swedish tobacco company in exchange for urging Mr. Dalli to soften restrictions on sales of a smokeless tobacco product.
A former police chief in Malta, John Rizzo, said in a recent interview that “there was enough evidence to substantiate a criminal case against John Dalli” but that he “cannot really explain” why Mr. Dalli was not charged in the tobacco case.
Even as that scandal unfolded, European Union investigators were looking into Mr. Dalli because he had taken three trips to the Bahamas in 2012 — including a round trip from Cyprus and back in one weekend — before he was forced to resign.
Investigators allege that the trips were related to a Ponzi-style scheme — nicknamed Gold Pool — led by Mr. Dalli’s friend Eloise Corbin, an American who had a long history of run-ins with the law and who boasted of connections to a rich Chinese family. (No one responded after a reporter knocked on Ms. Corbin’s door, and left a letter requesting an interview, at her home in Malta.)
Investigators say that Mr. Dalli and Ms. Corbin traveled together in 2011 and 2012 to a German health spa, and spent time together at a villa in the Bahamas, where he benefited from the use of an $8,000-a-month beachside villa that was not declared to the European Commission, his employer at the time.
Many of the investors thought their money was going to an entity called Tyre Ltd., which reported trading gold. Mr. Dalli’s daughters served on the board of the company, and its registered address was the same as a consultancy run by Mr. Dalli.
In 2011, Ms. Corbin invited an American friend, Debbie Wicker, to Malta. They had met in the Philippines on a Christian mission in 2002, and shared an interest in Chinese medicine. Ms. Wicker brought eight people from South Carolina, including Ms. Hayes, into Gold Pool. (A woman who answered the phone at a number listed for Ms. Wicker in South Carolina hung up when this reporter identified himself.)
During a visit to the Bahamas, Ms. Corbin introduced Mr. Dalli to Michael D. Brady, a founder of a Tea Party branch in South Carolina, as her business partner and as a European commissioner, and that “gave credibility to her and the whole investment scheme,” Mr. Brady wrote in an email.
“We were also told that these miners were Christian and for that reason were being pushed out by the larger miners,” said Mr. Brady, whose wife, Maria, briefly invested in the scheme.
Ms. Corbin, he recalled, would take a percentage of the profits to help orphans in the Philippines, and it would be a “legal and safe alternative to the stock market.”
Ms. Hayes, who is a friend of the Bradys, recalled, “Maria got out the Bible and looked up Tyre, and they’re saying Tyre is supposed to be the wickedest city. We should have right there stopped and said, ‘We better not invest.’ But stupid us.”
Another investor, James B. Geiger, who lives in Alabama and who invested $600,000, told European investigators that the “fact that John Dalli as E.U. commissioner was involved gave me the trust” he needed.
Mr. Geiger, who did not respond to requests for comment, is an organizer of the Republic for the united States of America, which denies the federal government’s legitimacy and says it is preparing a government-in-waiting to take power when the one in Washington eventually collapses.
Investigators who worked on the Dalli case wrote in their report that some victims of the fraud scheme were reluctant to talk because of their involvement in fringe political organizations.
Ms. Hayes, 72, has battled heart problems and a hernia and has had to give up annual cruises — often to the Bahamas — to keep up payments for medical care.
She said that her dividend payments stopped in December 2012. A former credit investigator for Ford Motor, she learned that Mr. Dalli had been ousted from his job in Brussels.
It wasn’t until February 2015 that Ms. Hayes gathered seven other investors around her dining room table. But hopes of recouping their investments drained away when one of them, Janie B. Moore, 69, distributed copies of an anonymous email alleging that Ms. Corbin had already spent large sums of the investors’ money to pay for indulgences like the rented Bahamas villa.
It was “a matter of time and the funds disappear,” the email warned.
The investors “realized at that point they had been suckered,” said Ms. Moore, who had invested $409,000, which she described as her life savings. She never received a dividend and recovered only $7,200 from her investment.
Ms. Moore says she is unable to buy a new car or travel. “Dalli’s living high on the hog and we have no money to even live on,” she said. “If anything breaks down, I am just stuck with it.”