31 C.F.R. § 100.5 – Mutilated paper currency.

(a) General. Lawfully held mutilated paper currency of the United States may be submitted for examination in accord with the provisions in this subpart. Such currency may be redeemed at face amount if sufficient remnants of any relevant security feature and clearly more than one-half of the original note remains. Fragments of such mutilated currency which are not clearly more than one-half of the original whole note or are lacking sufficient remnants of any relevant security feature will be redeemed at face value only if the Director, Bureau of Engraving and Printing, Department of the Treasury, is satisfied that the missing portions have been totally destroyed. The Director's judgment shall be based on such evidence of total destruction as is necessary and shall be final. Any submission under this subpart shall be deemed an acceptance of all provisions contained herein.
(b) Definitions. The following definitions are used in this subpart:
Mutilated currency is currency which has been damaged to the extent that:
1. (i) One-half or less of the original note remains; or
2. (ii) Its condition is such that its value is questionable and the currency must be forwarded to the Department of the Treasury for the examination by trained experts before any redemption is made.
  Unfit currency is currency which is unfit for further circulation because of its physical condition such as torn, dirty, limp, worn or defaced. Unfit currency should not be forwarded to the Department of the Treasury, but may be exchanged at commercial banks.