Answer
A contingent liability exists when an individual will be held responsible for payment of a debt, should another party, jointly or severally obligated, default on that payment. Unless the borrower can provide conclusive evidence from the debt holder that there is no possibility the debt holder will pursue debt collection against him or her should the other party default, the following rules apply to contingent liabilities:
1. Mortgage Assumptions. When a borrower remains obligated on an outstanding FHA-insured, VA-guaranteed, or conventional mortgage secured by a property that has been sold or traded within the last twelve months without a release of liability, or is to be sold on assumption without a release of liability being obtained, contingent liability must be considered unless:

a. The originating lender of the mortgage being underwritten obtains from the servicer of the assumed loan a payment history showing that mortgage has been current during the previous 12 months; or
b. An appraisal or closing statement from the sale of the property supports a value that results in a 75 percent LTV ratio [i.e., the outstanding balance on the mortgage loan (minus any UFMIP, if applicable) cannot exceed 75 percent of the appraised value or sales price].

2. Co-Signed Obligations. If the individual applying for an FHA-insured mortgage is a co-signer-or is otherwise co-obligated on a car loan, student loan, mortgage, or any other obligation - contingent liability applies unless the lender obtains documented proof that the primary obligor has been making payments during the previous 12 months on a regular basis and does not have a history of delinquent payments on the loan.

Handbook 4155.1: 4.C.5.a-e