Testing Maintenance Therapy for Small Cell Lung Cancer in Patients With SLFN11 Positive Biomarker

PRIMARY OBJECTIVE: I. To compare progression free survival (PFS) among participants with Schlafen family member 11 (SLFN11) positive extensive stage small cell lung cancer (ES-SCLC) randomized to atezolizumab or atezolizumab plus talazoparib as maintenance therapy. SECONDARY OBJECTIVES: I. To compare overall survival (OS) between the arms. II. To compare objective response rate (ORR) among participants with measurable disease between the arms, including complete response (CR) and partial response (PR) (confirmed and unconfirmed) by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. III. To evaluate the frequency and severity of adverse events within each treatment arm. TRANSLATIONAL MEDICINE OBJECTIVE: I. To bank specimens for future correlative studies. OUTLINE: Patients are screened for SLFN11 biomarker during Step 1: Screening Registration by submitting tumor tissue to MDACC. Patients with SLFN11 biomarker are registered to Step 2: Randomization and are randomized to 1 or 2 arms. ARM I: Patients receive atezolizumab intravenously (IV) over 60 (+/- 15) minutes on day 1. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive atezolizumab IV over 60 (+/- 15) minutes on day 1 and talazoparib orally (PO) once daily (QD) on days 1-21. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients may undergo magnetic resonance imaging (MRI) during screening. Patients undergo tumor biopsy while on study. Patients undergo computed tomography (CT) scan and blood sample collection throughout the study.