My grandfather just co-signed for me on a used honda civic about 2 months ago. Im the only one that drives the vehicle and i do have full coverage insurance on it that i pay for. My grandfather has been extremely concerned about me causing over $400,000 in damage or injury to someone else. now my insurance only covers 15,000. but what im trying to say is im 20 yrs old and if i was to cause over $400,000 in injury or damage to someone else, would the co-signer be liable if i couldnt afford the cost?