Cosignatory, co-signatory, cosigner, persons or state signing a treaty or other document jointly with others.  If a loan has a cosigner, and the borrower dies, that cosigner is considered liable for the debt. 
When you cosign a note, you are taking on someone else’s debt. Debt is an excess of liabilities over assets. The concept is really that of co-borrowing instead of just cosigning.  When you co-sign, you're not vouching for the person's good name or character. You're not promising to tell the creditor where to find the cardholder if those payments stop coming. You're agreeing to foot the bill. All of it. Along with fees and interest. 
c.1300, to make the sign of the cross. Sense of "to mark, stamp" is attested from mid-14c.; that of "to affix one's name" is from late 15c.