Creditors will accept debt negotiation for several reasons.  The first reason is getting something is better than getting nothing.  Debt negotiation is better than forcing a debtor into bankruptcy.  The creditor will receive nothing if the bankruptcy is allowed.  By negotiating the debt, the creditor will receive a percentage of what is owed.  They also will not have to expend more effort and money on trying to collect the debt.

A second reason for creditors accepting debt negotiations is the creditor has already figured it in as a cost of doing business.  As an example, the credit card companies know that a certain percentage of money owed to them will be written off.  The offset for these write-offs is charging a higher interest rate to many customers.  Credit card companies earn billions of dollars a year in profit.  They have accounted for negotiated debt reduction in their business plan.

A third reason, using the credit card companies as an example, the higher interest rates to cover write-offs, allows for more profit from those paying debtors.

Other businesses negotiate debts for basically the first reason.  Getting a debt settled is a means to get some money out of the debtor.  Clearing the books of bad or under performing debts keeps the business clean and is less costly in the long run. 

Creditors will accept debt negotiation or reduction when confronted with the reality of take this offer or get nothing.  The alternative is the debtor files for bankruptcy; it is allowed and the creditor receives nothing.  This is a huge incentive to negotiate.