This pilot phase I trial compares administration schedules of anti-programmed cell death-1 ligand 1 (PD-L1) monoclonal antibody MPDL3280A and stereotactic ablative radiotherapy in treating patients with stage IV non-small cell lung cancer. Monoclonal antibodies, such as anti-PD-L1 monoclonal antibody MPDL3280A, may block tumor growth in different ways by targeting certain cells. Stereotactic ablative radiotherapy, also known as stereotactic body radiation therapy, is a specialized radiation therapy that delivers a single, high dose of radiation directly to the tumor and may kill more tumor cells and cause less damage to normal tissue. Giving anti-PD-L1 monoclonal antibody MPDL3280A with stereotactic ablative radiotherapy may be a better treatment for non-small cell lung cancer. However, it is not yet known what the best administration schedule is for these treatments.