Does the surviving spouse have to repay a home equity loan if they are not listed as a borrower on the loan?

Yes in community property states and maybe in non-community property states.

If the state is a communal property state and the surviving spouse that is not a borrower had ANY benefit from the loan, that spouse is responsible for repayment (despite not being a borrowing party on the loan).

If the state is a non-communal property state, the estate of the deceased spouse will first be looked to in order to provide the funds to pay off all debts. If there are enough assets to cover the debt, the loan will be paid in full, regardless of the surviving spouse's wishes as the lender's rights come before those that may be beneficiaries to any estate proceeds.

If there are not enough assets to cover the loan, the lender may look to liquidate the asset (the surviving spouse's home) in order to satisfy the debt. If the home is NOT in the surviving spouse's name (either through joint tennancy or named ownership), the surviving spouse may not be able to intervene.