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

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma involving the gastroesophageal junction or gastric cardia * Central pathology review to determine evaluability of archived esophagogastroduodenoscopy (EGD)/biopsy sample * NOTE: If archived sample was collected \> 8 weeks prior to pre-registration (reg), is not available in a timely manner, or was collected outside of Mayo Clinic and considered unevaluable, then baseline EGD with primary tumor biopsy at Mayo Clinic must be performed unless clinically contraindicated; patient is allowed to enroll regardless of whether this Mayo Clinic tissue sample is evaluable; (Only 1 EGD with primary tumor biopsy performed at Mayo Clinic =\< 8 weeks prior to pre-reg is required) * NOTE: For both archival or newly obtained tissue, only biopsies are adequate (fine needle aspiration \[FNA\] is not adequate) * Willing to provide mandatory tissue samples for research purposes * Baseline imaging with an fludeoxyglucose (FDG)-positron emission tomography (PET) scan negative for distant metastatic disease must be obtained =\< 28 days prior to registration * Surgically resectable (T2N0, T3N0, Tany with node positivity, M0), as determined by endoscopic ultrasound (EUS) and the following minimum diagnostic work-up: * Whole-body PET/computed tomography (CT) (PET/CT of skull base to mid-thigh is acceptable) * EUS =\< 21 days prior to registration * NOTE: Patients may have regional adenopathy including para-esopha…