Olaparib and Ramucirumab in Treating Patients With Metastatic or Locally Recurrent Gastric or Gastroesophageal Junction Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * The patient must have histologically confirmed, gastric carcinoma, including gastroesophageal junction (GEJ) adenocarcinoma (patients with adenocarcinoma of the distal esophagus are eligible if the primary tumor involves the GEJ) * The patient has metastatic disease or locally recurrent, unresectable disease * The patient must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 * The patient must have experienced disease progression during or within 4 months after the last dose of chemotherapy for metastatic disease, during or within 6 months after the last dose of adjuvant chemotherapy, or have been intolerant of previous chemotherapy * The patient must have experienced disease progression or intolerance as outlined above after treatment with 1 or more prior chemotherapies * All previous treatments are acceptable as long as they did not contain bevacizumab, ramucirumab or PARP inhibitors * Elevation in tumor markers without radiographic evidence of disease progression is not satisfactory for progression on previous treatment * The patient is \>= 18 years of age * The patient has a life expectancy of \>= 16 weeks * Eastern Cooperative Oncology Group (ECOG) performance status score of 0-1 (Karnofsky \>= 60%) * Hemoglobin \>= 10 g/dL with no blood transfusions (packed red blood cells and platelet transfusions) in the past 28 days (within 28 days prior to administration of study treatment) * White blood cells (WB…