This label of co-signer is very often not understood by those who sign. Too many think that this label means shared or situationally responsible. It absoutely means neither.
A co-signer is a borrower.
A co-signer is totally and completely responsible for the complete repayment of the loan.
A co-signer is responsible for the entire term of the loan.
A co-signer will have this loan reported on their credit bureau report.
The only way for a co-signer to be relieved of the obligation is for the loan to be paid off in full, which can be accomplished by way of a refinance.
Co-signers are permitted on certain products and most commonly used by parents signing along with their children. Most often the children are buying their first home, but are lacking the credit history required. The underwriter might suggest, or the parents may suggest, that the parents also sign the note. With the parents' signature the overall credit strength of the loan is improved, as the loan now has additional borrowers with a more complete credit history, who would be contacted if and whenever a payment might be late.
The children would be the primary borrower and will be receiving any and all mail regarding the loan. The parents, most likely living in their own home, would not be receiving any of this mail, unless and until a payment becomes late.
The borrower side benefit to co-signing is to protect the inexperienced borrower from making a mistake that could result in derogatory payment history to the credit bureau or worse, a foreclosure or repossession.