Family Notification of Death, Injury, or Illness in Custody Act of 2021 This bill requires the Department of Justice (DOJ) to develop policies and procedures for notifying next-of-kin or other emergency contacts in the event of the death, or serious illness or serious injury, of an individual in custody. The bill requires DOJ to implement the policies and procedures at its detention agencies. Further, the bill requires DOJ to distribute model policies and procedures to state, territorial, tribal, and local detention agencies.