If the debt has any reported delinquencies or derogs, such as a charge-off or collection, then offers to pay can be used as an incentive to also remove any reported derogs.
Payment history is the highest-weighted scoring category, and linking offers to pay to clearing out derogs can result in significant score improvement.
If you can also negotiate a settlement for less, then you can include the provision that they also agree not to make any reporting of paid/dettled for less.
Your credit report will then appear the same in a manual review as it would if you paid in full.
