A lender will require a borrower to find a willing co-signer if it is worried about the borrower's ability to repay a loan. The co-signer takes responsibility for repaying the loan if the primary borrower does not. If the lender cannot collect from the borrower, the co-signer must repay the loan plus late fees, interest, or other charges the lender adds.
Loans are secured or unsecured. A secured loan is tied to the item purchased with the borrowed money, customarily. In the legal trade, the item in question is referred to as the security. Vehicle loans and property mortgages are common examples of secured loans. A credit card is a common example of an unsecured loan.
A vehicle or house may be purchased with borrowed money, but it is not the loan that gives the borrower or lender the right to possess the security. A title determines who has ownership rights to the vehicle or home.
For a vehicle purchased with a loan, the title will list the name of the lender. If the borrower defaults on the loan, the title (among other legal documents) will give the lender the right to repossess the vehicle. If a vehicle contains only the name of the primary borrower and the lender, then the co-signer (if any) has no rights to the vehicle. If the co-signer is listed on the vehicle's title, then he or she has the legal right to possess the vehicle.
For real property, the concept is the same as a vehicle loan, but details differ. However, the central point is the same — if the co-signer is listed on a real property's title, then he or she has some interest in that property. Rights to a property can be complex, and take half a semester to teach in law school, so it is beyond the scope of this answer to discuss an owner's possible rights to a property.
Your Question About Co-Signer Rights
You asked what rights a co-signer has to a security. The real question is, "Does the co-signer's name appear of the title?" If yes, then the co-signer has a right to the security. If the co-signer's name does not appear on the title, then the co-signer has no right to the security.
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