Nivolumab in Combination With Chemotherapy Pre-Surgery in Treating Patients With Borderline Resectable Pancreatic Cancer

Inclusion Criteria: * Histologically confirmed pancreatic adenocarcinoma * One of the following: * Borderline resectable disease. There are multiple definitions of borderline resectable pancreatic ductal adenocarcinoma (PDAC) including the MD Anderson definition and the criteria developed during the Consensus Conference sponsored by the American Hepato-Pancreato-Biliary Association, Society of Surgical Oncology, and Society for Surgery of the Alimentary Tract. Borderline resectable PDAC cases will be identified per the definition developed in the currently running inter-group pilot trial for borderline resectable pancreatic cancer (NCT01821612). Per this trial, borderline resectable PDAC is defined as the presence of any one or more of the following on computed tomography (CT): * An interface between the primary tumor and the superior mesenteric vein or portal vein (SMV-PV) measuring \>= 180 degrees of the circumference of the vessel wall * Short-segment occlusion of the SMV-PV with normal vein above and below the level of obstruction that is amenable to resection and venous reconstruction * Short segment interface (of any degree) between tumor and hepatic artery with normal artery proximal and distal to the interface that is amenable to resection and reconstruction * An interface between the tumor and superior mesenteric artery (SMA) measuring \< 180 degrees of the circumference of the vessel wall * Performance status of Eastern Cooperative Oncology Group (ECOG) of 0-1 * Therapy naive * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin \>= 9 g/dl * Serum total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) and aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Serum creatinine (sCr) =\< 1.5 x ULN or creatinine clearance (Ccr) \>= 40 mL/min as calculated by the modified Cockcroft-Gault formula * Peripheral neuropathy \< grade 2 Exclusion Criteria: * Locally advanced (clearly unresectable) or metastatic disease * Known status of human immunodeficiency virus (HIV) which is not well-controlled at the time of study eligibility * Untreated hepatitis B infection * Active infection or antibiotics within 48 hours prior to study * Currently active second primary malignancy or history of malignancy less than 5 years prior to the time of study eligibility (patients with history of skin cancers excluding melanoma will be eligible for participation) * Serious medical comorbidities such as New York Heart Association class III/IV cardiac disease, uncontrolled cardiac arrhythmias, myocardial infarction over the past 12 months * Known, existing uncontrolled coagulopathy. Patients who have had a venous thromboembolic event (e.g., pulmonary embolism or deep vein thrombosis) requiring anticoagulation are eligible IF: they are appropriately anticoagulated and have not had a grade 2 or greater bleeding episode in the 3 weeks before day 1 * Prior history of cerebrovascular accident or transient ischemic attack, or pre-existing carotid artery disease * Known pregnancy, nursing women or positive pregnancy test. Requirement for women of childbearing potential (WOCBP) must have a pregnancy test every 4 weeks and WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 24 hours prior to the start of nivolumab * Any prisoners, or subjects who are compulsory detained are excluded * Any condition that would preclude informed consent, consistent follow-up and compliance for the study participation