Providing Responsible Oversight of Trusts to Ensure Compensation and Transparency for Asbestos Victims Act of 2018 or the PROTECT Asbestos Victims Act of 2018 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 (reorganization). Among other things, the bill does the following: provides statutory authority for the U.S. Trustee Program within the Department of Justice to investigate the administration and operation of asbestos bankruptcy trusts; and creates new criminal offenses for making a false representation to, or a false claim for payment by, an asbestos bankruptcy trust.