With home prices rising, interest rates falling and builders building, some prominent housing advocates are calling for a new kind of loan for buyers with lower incomes or bad credit.

They’d like to call it the Dignity Mortgage, but it has another name — one that’s become more of an epithet since the housing crash: subprime.

Applicants might include people caught in the early stages of the mortgage meltdown who have since rebuilt their finances, said Faith Bautista, who heads the National Asian American Coalition.

“They lost their work, their homes and their credit scores four or five years ago,” Bautista said.

Since then, she said, many have found new jobs and saved up enough for a 10 percent down payment. But they can’t get a loan because lending standards remain tight — even for the Federal Housing Administration mortgages designed to help lower-income borrowers, Bautista said.

The proposal starts with the classic subprime trade-off: a higher rate for a higher-risk clientele. Borrowers would pay 1.25 percentage points above the going interest rate, maybe 4.75 percent if more creditworthy borrowers were paying 3.5 percent.

But the deal would get better if borrowers made timely payments for five years. At that point, the extra money they had paid in interest would be used to reduce the mortgage balance, and their rate would be cut to whatever borrowers with sterling credit and 20 percent down payments were charged at the time the loan was made.

Pattie Sibug of San Diego is among those who got caught short by the housing crash. By early 2010, the property improvement company she and her husband had owned for a dozen years had already seen its business fall off. Then a stream of work repairing foreclosed homes for a big bank dried up.

BID Construction wound up owing suppliers about $60,000 it could never fully repay, which ultimately ruined the couple’s personal and business credit scores. “It was 585 the last time I checked,” Sibug said of her score.

Sibug and her husband, Ollie, would like to buy the town house they are renting for $1,750 a month, and could come up with a 10 percent down payment. But they had to decline the owner’s recent offer to sell because they knew they couldn’t get financing.

“There’s got to be some kind of program to help you re-establish yourself,” Sibug said. “I’d be the first person in line if there was.”

Edward J. Pinto, a former Fannie Mae chief credit officer who argues that lax FHA lending helped feed the foreclosure crisis in low-income neighborhoods, said the Dignity Mortgage proposal “is a stupid and crazy idea — a poison pill.”

“Haven’t we learned anything from the cratering of our housing finance market?” said Pinto, a resident fellow at the American Enterprise Institute, a free-market think tank.

Bank officials continue their soul-searching over the mortgage misdeeds of the past and the prospects of the business.

“By being overly aggressive, the entire housing system caused a great deal of damage to the very people we were trying to help attain homeownership,” said Brian T. Moynihan, chief executive of Bank of America Corp.