Dear Dave: I called a creditor recently to settle an old debt. They offered a settlement but said it was their policy not to put settlement offers in writing. Should I accept the deal?
No way. If you don't have anything in writing, then you have no proof that they extended the offer or agreed to a specific amount. The only one who will have "proof" of anything in this scenario is the creditor, and that's just asking for trouble.
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My suggestion for handling this ridiculous situation goes something like this. Explain to them that you seem to have reached an impasse, because you have a policy of never accepting settlements and handing out money unless the settlements are in writing. No writing, no money! It's not a hard concept to understand, and it's fair to both parties.