Annette Alejandro just emerged from bankruptcy and doesn’t have a job, and her car was repossessed last year. Still, after spending her days job hunting, she returns to her apartment in Brooklyn where, in disbelief, she sorts through the piles of credit card and auto loan offers that have come in the mail.

“Even I wouldn’t make a loan to me at this point,” Ms. Alejandro said.

In the depths of the financial crisis, borrowers with tarnished credit like Ms. Alejandro were almost entirely shut out by traditional lenders. It was hard enough for people with stellar credit to get loans.

But as financial institutions recover from the losses on loans made to troubled borrowers, some of the largest lenders to the less than creditworthy, including Capital One and GM Financial, are trying to woo them back, while HSBC and JPMorgan Chase are among those tiptoeing again into subprime lending.

Credit card lenders gave out 1.1 million new cards to borrowers with damaged credit in December, up 12.3 percent from the same month a year earlier, according to Equifax’s credit trends report released in March. These borrowers accounted for 23 percent of new auto loans in the fourth quarter of 2011, up from 17 percent in the same period of 2009, Experian, a credit scoring firm, said.