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 ligand 2 (PD-L2) therapy

          -  Absolute neutrophil count (ANC) >= 1,500/mm^3

          -  Platelets >= 100,000/mm^3

          -  Hemoglobin >= 9 g/dL

               -  May receive transfusion to meet this goal

          -  Total serum bilirubin =< 1.5 x upper limit of normal (ULN) OR direct bilirubin =< ULN
             if total bilirubin levels > 1.5 x ULN

          -  Albumin >= 2.5 mg/dL

          -  Aspartate aminotransaminase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN OR
             =< 5.0 x ULN if liver metastases present

          -  Serum creatinine =< 1.5 x ULN OR creatinine clearance (if measured or calculated per
             institutional standard) >= 60 mL/min if creatinine levels > 1.5 x ULN

               -  Glomerular filtration rate (GFR) can also be used in place of creatinine or
                  creatinine clearance (CrCl)

          -  If not receiving anticoagulants: international normalized ratio (INR) OR prothrombin
             (PT) =< 1.5 x ULN; if on anticoagulant therapy: PT must be within therapeutic range of
             intended use of anticoagulants

          -  If not receiving anticoagulants: activated partial thromboplastin time (aPTT) =< 1.5 x
             ULN; if on anticoagulant therapy: aPTT must be within therapeutic range of intended
             use of anticoagulants

          -  Negative urine or serum pregnancy test (female of childbearing potential only)

               -  If the urine test is positive or cannot be confirmed as negative, a serum
                  pregnancy test will be required

          -  Female of childbearing potential: willing to use 2 methods of birth control or be
             surgically sterile, or abstain from heterosexual activity for the course of the study
             through 120 days after the last dose of study medication

               -  Childbearing potential defined as not being surgically sterilized or have not
                  been free from menses for > 1 year

          -  Male: use an adequate method of contraception starting with the first dose of study
             therapy through 120 days after the last dose of study therapy

        Exclusion Criteria:

          -  Anti-PD-1, anti-PD-L1, or anti-PD-L2 agents

          -  Prior radiation therapy within the field of the target lesion that in the opinion of
             the treating radiation oncologist would preclude further palliative radiation to a
             dose of 30 gray (Gy)

          -  Anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has
             not recovered (i.e., =< grade 1 or at baseline) from adverse events due to agents
             administered more than 4 weeks earlier

          -  Chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks
             prior to study day 1 or who has not recovered (i.e., =< grade 1 or at baseline) from
             adverse events due to a previously administered agent

               -  Note: Subjects with =< grade 2 neuropathy are an exception to this criterion and
                  may qualify for the study

               -  Note: If subject received major surgery, they must have recovered adequately from
                  the toxicity and/or complications from the intervention prior to starting therapy

          -  Live vaccine within 30 days of planned start of study therapy

               -  Note: Seasonal influenza vaccines for injection are generally inactivated flu
                  vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist)
                  are live attenuated vaccines, and are not allowed

          -  Immunosuppressive therapy within 7 days prior to the first dose of trial treatment

          -  Investigational device within 4 weeks of the first dose of treatment

          -  Currently receiving an investigational agent

          -  About to undergo palliative radiation for a symptomatic central nervous system (CNS)
             metastasis

          -  Systemic steroid therapy

          -  Hypersensitivity to pembrolizumab or any of its excipients

          -  Diagnosis of immunodeficiency

          -  Active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs)

               -  Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid
                  replacement therapy for adrenal or pituitary insufficiency, etc.) is not
                  considered a form of systemic treatment

          -  Known history of, or any evidence of active, non-infectious pneumonitis

          -  Current active infection requiring systemic therapy

          -  Known history of active tuberculosis (TB), human immunodeficiency virus (HIV) 1/2,
             hepatitis B or hepatitis C

          -  Known additional malignancy that is progressing or requires active treatment

               -  Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of
                  the skin that has undergone potentially curative therapy or in situ cervical
                  cancer

          -  Known active central nervous system (CNS) metastases and/or carcinomatous meningitis

               -  Subjects with previously treated brain metastases may participate provided they
                  are stable, have no evidence of new or enlarging brain metastases, and are not
                  using steroids for at least 7 days prior to trial treatment; this exception does
                  not include carcinomatous meningitis which is excluded regardless of clinical
                  stability

          -  History or current evidence of any condition, therapy, or laboratory abnormality that
             might confound the results of the trial, interfere with the subject's participation
             for the full duration of the trial, or is not in the best interest of the subject to
             participate, in the opinion of the treating investigator

          -  Known psychiatric or substance abuse disorders that would interfere with cooperation
             with the requirements of the trial

          -  Pregnant or breastfeeding (female only)