When a creditor becomes concerned about receiving continued payments because a debtor is having real financial problems, both parties may choose to reach an agreement to pay back the debt at a more affordable cost. This is known as debt settlement, because the creditor is settling for a lesser amount than what is owed in full. This is also commonly known as debt negotiation (but the "negotiation" is really the means of coming to a settlement).
Both the debtor and creditor have their reasons for settling the debt at a more affordable price:
The person in debt is doing their best to fix their financial situation without needing to declare bankruptcy. When they are unable to use a debt consolidation or credit counselling company to pay off what's owed, debt settlement is much less damning to their long-term credit than going bankrupt; and because the debt is paid off, those annoying phone calls from collection firms will stop.
For the creditor, going with a debt settlement proposition means they will be given a larger amount than they would were the person in debt made to go into bankruptcy, and can in fact save them money over using collection agencies and/or legal representatives trying to gather the full amount. This also means they'll get payment sooner than later.
Numerous debt management organizations will use a combination of both debt settlement and consolidation efforts when working with clients, negotiating individual debts as much as possible prior to combining them into one debt at a interest rate.