What is the term used when a mutual agreement allows for the cancellation of a debt and the creation of a new debt?

Novation is the term used when a mutual agreement allows for the cancellation of an existing debt and the creation of a new debt. This process involves a complete transfer of obligations and rights from one party to another, effectively replacing the original contract with a new one. For instance, if parties decide to change the terms of a loan, they can enter into a novation agreement where the original debt is extinguished, and a new debt with different terms is created.

In novation, all parties involved must consent for it to be valid, indicating that both the creditor and debtor agree to the terms of the new debt. This distinguishes novation from mere modifications or amendments, where existing terms may simply be altered rather than completely replaced.

Other terms mentioned, like subrogation, generally refer to a different context—specifically in insurance, where an insurer assumes the rights of a policyholder to recover claims from a third party. Modification and amendment typically pertain to altering existing agreements rather than creating completely new obligations, which is why they do not fit the definition described in the question.