Dignity for Detained Immigrants Act of 2021 This bill directs the Department of Homeland Security (DHS) to establish standards for facilities holding aliens in its custody, phases out using non-DHS facilities for such purposes, and contains other related provisions. The standards shall comply with the American Bar Association's Civil Immigration Detention Standards. The DHS Office of Inspector General (OIG) shall conduct periodic unannounced inspections of each facility and shall take various actions against noncompliant facilities, including imposing fines, cancelling contracts, and closing facilities. DHS shall report to Congress any death of an alien in its custody within 24 hours and conduct an investigation within 30 days that identifies policy changes that could reduce the likelihood of such a death. DHS is prohibited from entering into contracts for third parties to operate detention facilities or alternatives to detention programs and shall terminate existing contracts within three years of the bill's enactment. The bill establishes that OIG facility inspection reports and contracts for an outside entity to operate a detention facility are records available to the public under the Freedom of Information Act. DHS shall maintain certain information relating to detained aliens, including the alien's location and whether the alien was separated from family. The bill provides for various requirements and procedures related to detaining aliens, including (1) prohibiting DHS from detaining children, (2) imposing a presumption that an alien should be released, and (3) establishing that aliens in custody shall be subject to the least restrictive conditions. The bill also abolishes mandatory detention for asylum seekers.