Very little actually. They have the right to use the vehicle as long as they are current in their loan payments to the lender (who is the ACTUAL owner of the car, until the loan is paid off).
A borrower and co-borrower on a loan share benefit and liability equally. The only practical difference between the two is that loans are generally priced (interest rate or fees) based on the primary...
If there was a co-signer on the loan, then the co-signer will be responsible for the balance of the amount still owed. If not, then the lender can sue, or place a lien on the estate of the deceased...
You should think of them more accurately as obligations rather than rights. A co-borrower on a mortgage should ALWAYS be an owner by deed also. That way, if one co-signer leaves the remaining...
No, you can't use your spouse's income on a mortgage loan if she isn't going to "sign" it as a co-borrower. Only the incomes of those who sign for the loan are considered.