Federal Employees Civil Relief Act This bill establishes a framework to temporarily suspend certain judicial and administrative proceedings against a federal employee or contractor during a shutdown (i.e., any period in which there is more than a 24-hour lapse in appropriations affecting any federal agency or department). A federal worker who is furloughed or required to work without pay during a shutdown may apply to a court for a temporary stay, postponement, or suspension of any payment of rent, mortgage, tax, fine, penalty, insurance premium, student loan repayment, or other civil obligation or liability that the worker or individual owes or would owe during the duration of the shutdown. The Department of Justice many commence a civil action against any person who engages in (1) a pattern or practice of violating the requirements of this bill, or (2) a violation that raises an issue of significant public importance. A person aggrieved by a violation of this bill's requirements may also bring a private right of action.