Executives say borrowers receiving the letters are eligible, but they still have to prove they qualify. In order to be eligible, a borrower must be 60 days late on the mortgage payment as of Jan. 31, 2012. The borrower has to owe more on the mortgage than the home is currently worth, commonly known as being “underwater” on the mortgage, and the borrower’s loan must either be owned by Bank of America or serviced by Bank of America for an investor who is allowing the modifications.

In order to qualify for the modification, the borrower must answer the letter with full documentation of income, showing that under the terms of the modification they can still make the monthly payment. A borrower with no income would therefore not qualify. A borrower’s current monthly payment must be more than 25 percent of gross income, and the borrower must show they are unable to afford that.

“If you can afford to make your monthly payment and are choosing not to, you will not get this principal modification,” says Sturzenegger.

If the borrower qualifies, Bank of America will bring the monthly mortgage payment down to 25 percent of the borrower’s gross income. That could mean principal forgiveness well over $100,000, as there is no limit to the amount of the mortgage. If enough borrowers respond, it could cost Bank of America far more than it committed to in the settlement.

“Yes, we have the capability to go well beyond the $11 billion,” adds Sturzenegger.

Bank executives say that before choosing which borrowers will get the offer, they performed a net present value test on each loan, making sure that the principal reduction modification would net Bank of America or the investor who owns the loan more than foreclosing on the home. “It has to be fair to the investor as well,” says Sturzenegger.

Not all of the 200,000 borrowers who receive the letters are expected to respond. Executives say there is a level of fatigue among delinquent borrowers who have already received several notices or who may have gone through a failed modification process already. Some borrowers simply don’t want to stay in their homes, while others may think the offer is a scam.

“They have been contacted by a lot of other people, and this offer may appear too good to be true,” says Sturzenegger.

That’s why Bank of America is sending the letters by certified mail and trying to make the language as simple as possible. A sample letter obtained by CNBC shows a bring red box in the top corner labeled, “IMPORTANT” and simple language stating, “Qualifying customers may reduce their monthly payment by an average of 35 percent.”

Some 6,500 letters should be arriving in mailboxes across the country this week, with a wave of new letters going out every week until the end of the summer, when all 200,000 should have been mailed. Bank of America is staggering the mailings in order to handle the expected response. The bank has staffed up to handle the task, with 50,000 employees manning servicing desks, but the process will clearly take a lot of time. That’s why Bank of America has suspended any foreclosure actions against these 200,000 borrowers until the process is complete.

There are currently 5.59 million U.S. loans that are either delinquent or in the foreclosure process, according to Lender Processing Services. Bank of America services one million of those loans, but many of them are owned by Fannie Mae and Freddie Mac. Their regulator, Edward DeMarco of the Federal Housing Finance Agency, has yet to agree to principal reduction in loan modifications, despite harsh criticism from some lawmakers on Capitol Hill and increasing pressure from the White House.

Questions? Comments? RealtyCheck@cnbc.comAnd follow me on Twitter @Diana_Olick