What term describes a person who agrees to be primarily responsible for the debt of another?

The term that describes a person who agrees to be primarily responsible for the debt of another is "Surety." In legal contexts, a surety is specifically someone who takes on the responsibility for the debt or obligation of another party, often in a formal agreement. This means that if the principal debtor fails to fulfill their obligations, the surety is the first person a lender can seek for repayment before looking to the original borrower.

In this role, the surety assumes a more significant risk because they are obligated to pay the debt regardless of whether the primary borrower can do so. This contrasts with a guarantor, who typically provides an additional layer of responsibility, only stepping in after efforts to collect from the primary debtor have been exhausted.

In this context, distinguishing between these roles is essential, as they indicate different levels of responsibility in financial agreements. This is why "Surety" is considered the correct term for someone who is primarily responsible for another's debt.