Husband cosigned for a car loan and I need to know the legal ramifications for me.

Assuming that the law of Tennessee is the same as the law of New York in this area, you personally would not be liable on the loan, or any other personal obligation of your husband other than what are considered "necessaries."  For example, if your husband was treated for a heart attack, you would probably be personally responsible for the medical bills if he, for whatever reason, couldn't pay, but you would have no personal responsibility for his "fruit of the month club" subscription. While you personally would not be responsible for the loan, your husband's estate would remain liable which, if you are the sole beneficiary of the estate, might amount to the same thing in practical terms.