The bank already faces a £40m bill, to pay a fine plus compensation for NHFA's mis-selling of investment bonds designed to cover care home fees.
Now the bank has said it will consider complaints from before when it took over NHFA in 2005.
Claims will be accepted from elderly customers or their families.'Sympathetic'
The Financial Services Authority fined HSBC £10.5m on Monday for NHFA's unsuitable sales of financial products to people expected to die before the recommended investment period was up.
The bank said it was likely to pay an estimated £29m in compensation to victims.
NHFA had 11,000 customers while it was owned by HSBC, of whom 2,485 were possible victims of the poor advice.
The bank will now accept complaints going back to 1991, during which time NHFA dealt with around 9,000 customers.
"We will take responsibility for all NHFA customers - including those from before HSBC bought the company in 2005 - to ensure that this issue is entirely resolved," said Brian Robertson, chief executive of HSBC Bank.
"I am profoundly sorry about what happened at NHFA and it is only right and proper that we stand fully behind these customers.
"Many customers will be rightly concerned that they, or indeed their relatives, might not have received appropriate advice from NHFA, so we will certainly look at each complaint individually and sympathetically."
There is no indication of the extent of mis-selling during that period. Many of the victims are likely to have died, so HSBC will take complaints from surviving family members.
Customers who signed up from April 2004 will receive letters from HSBC and do not need to take any action.
Any customers of NHFA from before April 2004 who wish to complain should e-mail NHFA@hsbc.com or write to NHFA, HSBC Bank Plc, PO Box 1888, Coventry, CV3 9WN, giving as much detail as possible about the customer in question.