Providing Responsible Oversight of Trusts to Ensure Compensation and Transparency for Asbestos Victims Act of 2021 or the PROTECT Asbestos Victims Act of 2021 This bill modifies several aspects of the asbestos bankruptcy trust system. An asbestos bankruptcy trust is established when a company subject to asbestos-related liability files for bankruptcy under chapter 11. The bill allows the U.S. Trustee Program within the Department of Justice to investigate the administration and operation of asbestos bankruptcy trusts. Additionally, it creates new criminal offenses for making a false representation to, or a false claim for payment by, an asbestos bankruptcy trust. Finally, an administrator of an asbestos bankruptcy trusts must report any Medicare benefits entitled to a claimant to the Centers for Medicare & Medicaid Services.