Ulster Bank is to write to 2,000 people in arrears telling them if they sell their homes they will not be pursued for the outstanding debt if they are on low incomes and eligible for social housing.
The commitment is made in a document which will be sent to people who have not communicated with the bank regarding their outstanding mortgage payments.
Lobby groups acting for those in arrears have argued banks need to be more realistic about writing off debts for some people.
Ulster Bank is beginning an initiative today to encourage those who are in default, but have no contact with the bank, to communicate with the lender.
It says if people are eligible for social housing and sell their homes they will not be pursued for the outstanding debt.
For those on higher incomes who sell their homes the bank says it will agree a fair process regarding the residual borrowings.
It is understood this could involve writing off some or all of the debt but it will vary on a case-by-case basis.
Ulster Bank Chief Risk Officer Stephen Bell said the bank's primary objective is to ensure people in difficulty remain in their homes on an affordable arrangement.
In a statement Mr Bell said: "While we are seeing increases in repossessions through vacant and abandoned properties, we do not want to see an increase in forced repossessions.
"We hope that people in difficulty find our commitments to be clear, comforting and choose to accept our help. However, it is vital that our approach is fair for all customers - both those maintaining their home loans and those who are in difficulty."