By Laura Saunders 

The Internal Revenue Service's announcement Tuesday of a data breach affecting more than 100,000 households has prompted fresh complaints from victims of tax identity theft about delayed refunds, red tape, cumbersome IRS procedures and continued effects on their finances.

Tax ID theft occurs when criminals steal personal information and use it to claim a tax refund in a taxpayer's name before he or she files. Many refunds are put on debit cards that can be hard to trace, experts say. IRS Commissioner John Koskinen said the agency assisted 875,000 victims of tax ID theft in the fiscal year ended Sept. 30. The government lost at least $5.8 billion to refund scams in 2013, according to the Government Accountability Office.

Rick Yost, a tire salesman from Palm City, Fla., said his troubles began when he received an unsolicited Green Dot Corp. prepaid debit card in the mail in March. It turned out, Mr. Yost learned, that a $9,856 tax refund had been claimed in his name by a fraudster who obtained Mr. Yost's date of birth and Social Security number. The criminal opened the account with $20 and withdrew the tax refund as soon as it posted, he said.

Getting that information wasn't easy, however. Mr. Yost couldn't talk to a person at Green Dot without supplying part of his Social Security number--"which I was reluctant to do, given the circumstances," he said.

When he did reach a representative, he said he was frustrated to learn that the firm never verified personal information about him that was required to open an account--and most of it didn't match his actual information.

A spokeswoman said Green Dot is looking into the case.

He also learned he would have to file separate legal affidavits with the IRS and other agencies, notify credit bureaus, and file his 2014 tax return on paper. He is about to do so--and might have to wait six months for his federal refund of several thousand dollars.

"We are the ones who are inconvenienced, not the thieves," said Mr. Yost. He said he asked an IRS staffer working on his case why no red flag was raised by the change from longtime direct-deposit information to a debit card. The staffer responded, "We're working on that!," according to Mr. Yost.

A spokeswoman for the IRS said the agency is continually adjusting its fraud filters.

Vicki Niesen, a chemical engineer who works with an oil firm in Houston, believes her ID theft began when her husband's 2014 W-2 information was stolen through Get Transcript, the compromised IRS application that prompted Tuesday's announcement.

The false return filed in their names, she said, had her husband's 2014 salary information "to the dollar"--although the thieves included $28,000 of Social Security income in the false return. It claimed a refund of $26,424.

Complaining of the IRS's "idiocy," Ms. Niesen said: "The questions to open 'Get Transcript' can easily be obtained through a credit report, and obviously many people check your credit."

The IRS said it would contact the 104,000 taxpayers whose information was compromised, as well as the 100,000 for whom attempts were unsuccessful. The first group will be offered credit monitoring, while the second will be warned that thieves have their personal information.

Frank Abagnale, a noted cybersecurity expert, suggests that victims remain wary for years. "Stolen identities are like fine wine: the older they are, the more valuable they are. These identities will be kept and used years from now to perpetrate fraud," he says. (As a young man, Mr. Abagnale was convicted of fraud-related crimes and served time in French, Swedish, and U.S. prisons. His early life was portrayed in the film "Catch Me If You Can.")

He also cautioned that the organized criminal groups likely behind the ID thefts probably wouldn't use it for credit-card fraud, which could be easily detected by credit monitoring.

"Instead, they will use stolen identities to file for government benefits such as Medicaid and SNAP in states where the true identities don't reside--so the fraud will never appear on a credit report," he said.

Write to Laura Saunders at laura.saunders@wsj.com