No one was more surprised than Thomas Carpenito with the credit-card invitation that landed in his mailbox earlier this year.

The 27-year-old deli owner from White Plains, N.Y., had about $10,000 in old debts and a credit rating 200 points below "good." He recalled thinking the post office had delivered the letter to the wrong house.

Far from a mistake, the offer was part of a controversial and growing partnership between debt collectors and banks that profits both. To get the new credit card, Mr. Carpenito agreed to repay $400 on a seven-year-old debt that had expired under New York's statute of limitations.

"It was totally worth it," he said. Having no credit cards made Mr. Carpenito feel "like dirt," he said, especially when out on dates. His new credit card, stamped with the MasterCard Inc. logo, was offered by Jefferson Capital Systems LLC, the debt-collection arm of CompuCredit Holdings Corp., in Atlanta.

CompuCredit, a leader in the business, collected about $15 million in newly resurrected debts and fees by issuing credit cards to people with banged-up credit in the first nine months of this year, according to a securities filing. It also has drawn scrutiny by federal authorities for allegedly deceptive practices.

Many U.S. banks, hungry for new revenue streams, are eager partners. They receive fees and higher-than-average interest rates by granting debt collectors access to their license with MasterCard. The debt companies typically agree to cover losses to banks if borrowers stop paying.

Some lenders say borrowers have a moral obligation to pay their debts even if they are no longer legally responsible. Others are leery about subprime borrowers. But the debt-driven credit cards show some banks tiptoeing back into subprime lending after suffering big losses during the financial crisis.

Collectors aren't afraid of the risks in issuing new credit cards because they instantly turn a profit on virtually worthless debts—purchased for pennies on the dollar—when people agree to start making payments on them. The credit-card agreements essentially create assets out of thin air.

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