Adding Nivolumab to Usual Treatment for People With Advanced Stomach or Esophageal Cancer, PARAMUNE Trial

Inclusion Criteria: * Participants must have advanced or locally unresectable gastric, gastroesophageal junction or esophageal adenocarcinoma * Participants must have PD-L1 CPS (Combined Positive Score) ≥ 1. This test would have been performed as part of standard of care (SOC) pathology testing, using tissue obtained within two years prior to registration and collected prior to or after a frontline regimen * Participants must have a histologically confirmed diagnosis of microsatellite stable (MSS) and HER2 negative gastric, gastroesophageal junction, or esophageal adenocarcinoma * Participants must have documented unresectable and/or metastatic disease on CT or MRI imaging completed prior to registration. Imaging must have been completed within 28 days prior to registration for participants with measurable disease. CT scans or MRIs used to assess non-measurable disease must have been completed within 42 days prior to registration. All disease must be assessed and documented on the Baseline Tumor Assessment Form * Participants with treated brain metastases must have no evidence of progression on the follow-up brain imaging after central nervous system (CNS)-directed therapy. All treatment for brain metastases must have been completed at least 28 days prior to registration * Participants must have disease progression or intolerance to frontline standard of care (SOC) chemotherapy plus either nivolumab, pembrolizumab or any other PD-1 or PD-L1 inhibitor. Peri-operative chemotherapy plus nivolumab, pembrolizumab or any other PD-1 or PD-L1 inhibitor will count as one line if disease progression occurs while on the therapy or within 6 months of completing the chemotherapy plus nivolumab or pembrolizumab or other PD-1/PD-L1 inhibitor cycle * Participants must not have received more than one prior line of systemic therapy defined as chemotherapy plus either nivolumab, pembrolizumab, or any other PD-1 or PD-L1 inhibitor, in the stage IV or unresectable setting. Peri-operative or adjuvant nivoluamb or other PD-1/PD-L1 inhibitors would count as one prior line of systemic therapy if patients progressed while on nivolumab (or other PD-1/PD-L1 inhibitors) or within 6 months of stopping it * Note: Radiation or any other regional therapy options done to address local residual disease or metastatic disease would not count as a line of therapy. Maintenance therapy with a different form of fluoropyrimidine (i.e. switching from capecitabine to fluorouracil \[5FU\]) would not count as another line of therapy * Participants must not have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of registration. Inhaled or topical steroids and adrenal replacement doses \< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Participants are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \< 10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted, as long as there has been a washout period for corticosteroids of ≥ 7 days prior to registration * Participants must not have prior significant immunotherapy related adverse events requiring permanent discontinuation of the immunotherapy agent including events like pneumonitis, myocarditis, renal failure, Guillain barre syndrome, or myasthenia gravis. Participants with endocrinopathy events leading or not to replacement steroids, thyroid hormone, insulin, or cortisol are eligible * Participants must not have received a live attenuated vaccination within 28 days prior to registration * Participants must not have had a major surgery within 28 days or subcutaneous venous access device placement within 7 days prior registration * Participants must have fully recovered from the effects of prior surgery in the opinion of the treating investigator. Any participants with postoperative bleeding complications or wound complications from a surgical procedure performed in the last eight weeks should be excluded * Participants must not have plans to undergo elective or planned major surgery during the clinical trial * Participants must not have active bleeding or prior history of gastrointestinal (GI) perforation, fistula or significant GI bleeding (requiring transfusion, endoscopic or surgical intervention) within 84 days prior to registration * Participants must not be planning to receive any concurrent chemotherapy, immunotherapy, investigational agents, biologic or hormonal therapy for cancer treatment while receiving treatment on this study * Participants must not have a history of a grade 3 or 4 allergic reaction attributed to humanized or human monoclonal antibody therapy * Participants must not have a history of grade 3 or 4 immunotherapy related toxicities with the exception of hormonal abnormalities like thyroiditis or thyroid derangements * Participants must be ≥ 18 years old * Participants must have Zubrod Performance Status of 0-2 * Participants must have a complete medical history and physical exam within 28 days prior to registration * Leukocytes ≥ 2 x 10\^3/uL (within 28 days prior to registration) * Absolute neutrophil count ≥ 1.2 x 10\^3/uL (within 28 days prior to registration) * Hemoglobin ≥ 9.0 g/dL (within 28 days prior to registration) * Platelets ≥ 100 x 10\^3/uL (within 28 days prior to registration) * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to registration) unless history of Gilbert's disease. Participants with history of Gilbert's disease must have total bilirubin ≤ 5 x institutional ULN * Aspartate aminotransfe