Chase, Bank of America and the other big lenders are negotiating with the Obama administration and the nation’s attorneys general over foreclosures. Debt forgiveness and the moral hazard question of who deserves to be helped are among the most contentious issues.

The banks say cutting mortgage balances would be unfair to borrowers who remain current as well as impractical because so many loans are securitized into pools owned by investors. Bank of America’s chief executive, Brian T. Moynihan, told the attorneys general in April that cutting principal for current borrowers would send the wrong message to all those who have struggled to pay their bills. His counterpart at Chase, Jamie Dimon, bluntly said it was “off the table.”

Having an option ARM loan, however, apparently qualifies the borrower for special help. The loans, with their low initial payments and “teaser” interest rates, were immediately popular with buyers who could not afford or did not want to pay the soaring prices on houses. The problem was, eventually the rate would reset or the loan balance would have to be paid in full. “Nightmare Mortgages” they were called in a 2006 BusinessWeek cover piece.

Option ARMs were never quite as bad as predicted, partly because the crisis pushed down interest rates so far that the resets were relatively mild. Many owners did default on them, but others, like Ms. Giosmas, were quite happy to pay less for years than they would have under a conventional loan. She used option ARMs on her investment properties too.

“They saved me,” she said. “Why would I want to pay a lot more every month? I’d rather have it in my pocket.”

The concern the banks are showing for those who might get in trouble contrasts sharply with their efforts toward those already foreclosed. Bank of America and Chase were penalized last month by regulators for doing a poor job modifying mortgages in default.

Adam J. Levitin, a Georgetown University law professor, said these little-publicized programs were more evidence that the banks were behaving in contradictory and often maddening ways.