When debt problems spiral out of control, the costs involved in terms of interest payments and charges can quickly mount up, and in extreme cases you can end up owing at least as much in these costs as you originally borrowed. This is especially true of credit cards, where making the minimum repayments means that nearly all of your money goes towards servicing your debt costs without actually reducing what you owe.
Problem debts can easily become a treadmill of demand letters, missed payments, and stress. This situation benefits neither the debtor nor the creditor, and if you sincerely can't pay what you owe, then many creditors will agree to write off some of your debt under an arrangement known as a 'full and final settlement'. Even though you won't be fully clearing what you owe, creditors will usually take the pragmatic view that receiving some amount of a problem debt is better than receiving nothing, which might very well happen if bankruptcy becomes necessary.
The most usual scenario for making a full and final settlement is when a debtor comes into a windfall - maybe an inheritance, a share issue, or even the proceeds of a remortgage. This lump sum can then be offered as a payment to a creditor, with the explicit undertaking that by accepting this payment, the remaining debt will be written off and no further recovery action will be taken.
The amount that a creditor is willing to take as a final settlement will depend on a number of things, including how much of a proportion of your debt you're offering to pay off, how long the debt has been in arrears, and how likely they think alternative recovery methods would be to ensure a greater repayment.