Niraparib, Temozolomide and Atezolizumab in Treating Patients With Advanced Solid Tumors and Extensive-Stage Small Cell Lung Cancer With a Complete or Partial Response to Platinum-Based First-Line Chemotherapy

Inclusion Criteria: * Willing and able to provide informed consent. * Cytologically or histologically confirmed advanced and incurable solid malignancy. * For the Phase 1b, Part 2 cohort, participants must have a tumor type for which atezolizumab is an Food and Drug Administration (FDA) approved therapy. * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1. * Able to swallow the study drugs, has no known intolerance of study drugs or excipients, and able to comply with study requirements. * Absolute neutrophil count (ANC) \>= 1,500 /mcL. * Platelets \>= 100,000 / mcL. * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 4 weeks of first dose). * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 30 mL/min for participants with creatinine levels \> 1.5 X institutional ULN. (Glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]). * Creatinine clearance should be calculated using the standard Cockcroft and Gault equation. * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN. * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for participants with liver metastases. * Albumin \>= 2.2 mg/dL. * International Normalized Ratio (INR) or Prothro…