Pembrolizumab, Combination Chemotherapy, and Radiation Therapy Before Surgery in Treating Adult Patients With Locally Advanced Gastroesophageal Junction or Gastric Cardia Cancer That Can Be Removed by Surgery

Exclusion Criteria

• •Tumor characteristics - any of the following are excluded:
• •* Evidence of distant metastases
• •* Tumors whose location is restricted to the tubular esophagus (i.e., without involvement of the GEJ or cardia)
• •* Tumors whose proximal end are at the level of the carina or higher
• •* Invasion of the tracheobronchial tree or presence of tracheoesophageal fistula
• •* Palpable supraclavicular nodes, biopsy-proven involvement of supraclavicular nodes, or radiographically involved supraclavicular nodes (\> 1.5 cm in greatest dimension)
• •* T1N0M0, T4Nany, or in situ carcinoma
• •* Tumor must not extend 5 or more cm into the stomach
• •Received prior treatment or receiving current treatment for this malignancy
• •Prior radiation to chest or abdomen, or to \> 30% of the marrow cavity
• •Inadequate caloric or fluid intake whereby there is a current or likely future need for enteral or parenteral feeding during chemoradiation or the preoperative period
• •Major surgery =\< 4 weeks prior to registration
• •Active autoimmune disorders, including patients known to be human immunodeficiency virus (HIV) positive, or those requiring chronic steroid administration (excluding inhaled steroids)
• •Uncontrolled diabetes (i.e., will interfere with the performance of the FDG PET/CT scans)
• •Prior allergic reactions to drugs containing Cremophor, such as teniposide or cyclosporine, or study drugs involved in this protocol, or to a monoclonal antibody or prior hypersensitivity to platinum-containing agents
• •Heart conditions - any of the following:
• •* Any atrial fibrillation =\< 3 months prior to registration
• •* Unstable angina =\< 12 months prior to registration
• •* Prior symptomatic congestive heart failure
• •* Documented myocardial infarction =\< 6 months prior to registration (pretreatment electrocardiogram \[ECG\] evidence of infarct only will not exclude patients)
• •* Prior significant ventricular arrhythmia requiring medication
• •* Prior 2nd or 3rd degree heart block or other types of clinically significant conduction delay =\< 6 months prior to registration
• •* Clinically significant pericardial disease (including pericardial effusion, pericarditis) or cardiac valvular disease =\< 12 months prior to registration
• •* NOTE: As part of history and physical, all patients must be assessed for signs or symptoms of cardiac disease, or for prior history of cardiac disease; these conditions include but are not limited to diseases related to cardiac valves, pericardium, myocardium, atrioventricular delays or arrhythmias; it is strongly recommended that signs or symptoms of potentially clinically significant disease be evaluated with comprehensive cardiac echo
• •Prior pancreatitis that was symptomatic or required medical intervention =\< 6 months prior to registration (known toxicity of pembrolizumab)
• •Prior enteritis that was symptomatic or required medical intervention =\< 6 months prior to registration (known toxicity of pembrolizumab)
• •Uncontrolled hyper/hypothyroidism or hyper/hypocorticism =\< 6 months prior to registration (known toxicity of pembrolizumab)
• •Pulmonary conditions - any of the following:
• •* Respiratory condition that required any oxygen supplementation =\< 6 months prior to registration
• •* Prior or current pneumonitis
• •* Clinically significant pulmonary hypertension =\< 12 months prior to registration
• •* Lung infection requiring treatment =\< 3 months prior to registration
• •* Pulmonary embolism requiring treatment =\< 6 months prior to registration
• •* Pleural effusion requiring drainage =\< 12 months prior to registration
• •Prior fistula within thorax, including bronchoalveolar or esophageal
• •Body mass index (BMI) \>= 35 mg/m\^2 =\< 56 days prior to registration
• •Pre-existing motor or sensory neurotoxicity greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1
• •Acute bacterial, viral, or fungal infection requiring treatment at the time of registration
• •Active infection or other serious underlying medical condition which would impair the ability of the patient to receive the planned treatment
• •Uncontrolled intercurrent illness including, but not limited to, psychiatric illness/social situations, or other co-morbid systemic illnesses or severe concurrent diseases which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
• •Prior malignancy =\< 5 years prior to registration (except non-melanotic skin cancer or carcinoma-in-situ of the cervix) (must be disease free for a minimum of 5 years); if there is a history of prior malignancy, patient must not be receiving other specific treatment (other than hormonal therapy) for cancer
• •Dementia or altered mental status that would prohibit the understanding and giving of informed consent
• •Any of the following because this study involves an agent where the genotoxic, mutagenic and teratogenic effects are unknown:
• •* Pregnant or breastfeeding
• •* Patient of childbearing potential who is unwilling to employ adequate contraception
• •Received live vaccine =\< 30 days prior to registration