This phase II trial studies how well trifluridine/tipiracil and oxaliplatin work as the first line of treatment (induction) in treating patients with esophageal or gastroesophageal junction adenocarcinoma that can be removed by surgery (resectable). Drugs used in chemotherapy, such as trifluridine/tipiracil and oxaliplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading.

PRIMARY OBJECTIVE:

-Evaluate the pathologic complete response (path CR) rate in participants with esophageal and gastroesophageal junction (GEJ) adenocarcinoma when trifluridine and tipiracil hydrochloride (trifluridine/tipiracil [TAS-102]) and oxaliplatin are used as induction chemotherapy prior to surgical resection.

SECONDARY OBJECTIVES:

• Evaluate the 2-year disease-free survival (DFS) and the 2-year overall survival (OS)
• To determinate the safety and tolerability of induction chemotherapy with trifluridine/tipiracil (TAS 102) and oxaliplatin followed by standard chemoradiation and surgery
• Evaluate the metabolic response to induction chemotherapy with TAS 102 and oxaliplatin in participants with esophageal and gastroesophageal junction (GEJ) adenocarcinoma prior to standard chemoradiation and surgical resection

EXPLORATORY OBJECTIVE:

-Correlate circulating tumor deoxyribonucleic acid (DNA) levels with disease recurrence and metabolic response on positron emission tomography (PET) computed tomography (CT).

OUTLINE:

Patients receive oxaliplatin intravenously (IV) over 2 hours on day 1 and trifluridine and tipiracil hydrochloride orally (PO) twice daily (BID) on days 1-5. Treatment repeats every 14 days for 3 cycles in the absence of disease progression or unacceptable toxicity. Patients then undergo standard of care chemoradiation therapy followed by surgery.

After completion of study treatment, patients are followed up every 3-6 months for years 1-2, every 6-12 months.

Inclusion Criteria:

• Must have histologically proven loco-regional esophageal or gastroesophageal junction adenocarcinoma
• Endoscopic ultrasound (EUS), or clinically determined node-positive disease with any T-stage or T3-T4a with any N stage: Patients with EUS T4b and any M1 cancer will not be included
• Must have potentially resectable disease
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1
• Hemoglobin >= 9 g/dL
• Absolute neutrophil count >= 1500/mm^3
• Platelet count >= 100,000/mm^3
• Creatinine < 1.5 upper limit of normal (ULN)
• Bilirubin < 1.5 x ULN
• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3 x ULN
• Capacity to take oral tablet(s) without difficulty
• Participants of child-bearing potential must agree to use highly effective contraceptive methods (e.g., hormonal plus barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure

Exclusion Criteria:

• Prior chemotherapy, thoracic radiotherapy or prior surgical resection for an esophageal tumor
• Participants with known metastatic disease
• Any concurrent active malignancy that requires active systemic intervention
• Grade 2 or higher peripheral neuropathy
• Participants who have had major surgery or field radiation within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
• Received an investigational agent within 4 weeks prior to enrollment
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Grade 3 or higher hypersensitivity reaction to oxaliplatin or grade 1-2 hypersensitivity reaction to oxaliplatin not controlled with premedication
• Patient previously treated by TAS 102 or history of allergic reactions attributed to compounds of similar composition to TAS 102 or any of its excipients
• Hereditary problems of galactose intolerance; e.g., Lapp lactase deficiency or glucose galactose malabsorption
• Pregnant or nursing female participants
• Unwilling or unable to follow protocol requirements
• Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug