When borrowers default on their mortgages, lenders foreclose and sell the homes to recoup their money. But when homes sell for less than the value of their mortgages and home equity loans  a situation known as a short sale  lenders with first liens must be compensated fully before holders of second or third liens get a dime.

In places like California, Nevada, Arizona and Florida, where home prices have fallen significantly, second-lien holders can be left with little or nothing once first mortgages are paid.

In December, 5.7 percent of home equity lines of credit were delinquent or in default, up from 4.5 percent in 2006, according to Moody’s Economy.com.

Lenders and investors who hold home equity loans are not giving up easily, however. Instead, they are opposing short sales. And some banks holding second liens are also opposing refinancings for first mortgages, a little-used power they have under the law, in an effort to force borrowers to pay down their loans.

“Acknowledging a loss is the most difficult thing to do,” said Micheal Thompson, the executive director of the Iowa Mediation Service, which has been working with delinquent borrowers and lenders. “You have to deal with the reality of what you are facing today.”

While he has been able to strike some deals, Mr. Thompson said that many mortgage companies he talks with refuse to compromise. Holders of second mortgages often agree to short sales and other changes only if first-lien holders pay them a small sum, say $10,000, or 10 percent, on a $100,000 debt.

Disagreements arise when the first and second liens are held by different banks or investors. If one lender holds both debts, it is in their interest to find a solution.