Pembrolizumab and Palliative Radiation Therapy in Treating Patients With Metastatic Esophagus, Stomach, or Gastroesophageal Junction Cancer

Inclusion Criteria: * Documented informed consent of the participant * Willing to provide tumor tissue amenable to ultrasound or computed tomography (CT)-guided biopsy for biomarker analyses * Patients with malignant ascites are permitted to participate and provide ascites samples for biomarker analyses * Patents receiving radiation to a single metastatic site in which only the primary tumor is accessible for biopsy by endoscopy will also be eligible * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 * Life expectancy of \>= 3 months * Diagnosis of metastatic squamous cell carcinoma and/or adenocarcinoma of the esophagus, gastroesophageal junction, or stomach in need of palliative radiotherapy to the primary tumor or a single metastatic site for symptoms such as pain, dysphagia, and/or gastrointestinal bleeding * Patients with adenocarcinoma histology and known human epidermal growth factor receptor 2 (HER2) overexpressing disease are permitted to participate if the progressed or are intolerant of prior trastuzumab-containing therapy * Measurable metastatic sites of disease outside of the target lesion undergoing palliative radiation based on RECIST 1.1 as assessed by the investigator * Have no limits on prior lines of therapy or may be treatment-naive if in need of palliative RT provided the patient has not received prior anti-programmed cell death protein 1(PD-1), anti-programmed cell death 1 ligand 1 (PD-L1), or anti-programmed cell death 1 li…