Option 2 - Agree with the bank's proposal
Some people see the bank as imposing some agreement on them. But the reality is that a borrower has an obligation to repay the loan. The agreement reached with the bank does not impose any extra legal obligation which they did not already have.
The bank's purpose in getting the borrower to sign this agreement is to make sure that they fully realise that the bank is giving permission to sell but is not writing off the shortfall. It prevents the borrower from claiming at some later stage that the bank said that they would not pursue the shortfall.
Option 2A - Negotiate the bank's proposal
In most cases, the banks seem happy enough to accept repayment of the shortfall over the remaining period of the mortgage at the mortgage rate. In other cases, they try to get the shortfall repaid much sooner. In such cases, you should ask to extend it.
If you have good salaries, the bank will pursue the shortfall.
If you are in dire straits, they can't get blood out of a stone, so while they won't write it off, they probably won't pursue it either.
If you have a cheap tracker, you may be able to get the bank to write off some of the shortfall. But if you have a cheap tracker, it's very likely that you are much better off retaining the property, and renting it out.
If you do not want to retain the property as an investment, then you should accept the bank's proposal
As it does not give you any additional legal obligations, you should accept the bank's proposals.
You will be able to negotiate a deal on an unsecured loan much more easily than on a secured mortgage. For example, if a relative agrees to pay a lump-sum to clear the debt, the lender would probably grab it.
If you have to avail of the new Personal Insolvency Act, it is likely that a Debt Settlement Arrangement for unsecured debts will be much simpler to agree than a Personal Insolvency Arrangement for a secured mortgage.
If you choose to avail of UK bankruptcy, then it is much simpler if the Official Assignee does not have to deal with a property and a mortgage.