Comparison of Chemotherapy Before and After Surgery Versus After Surgery Alone for the Treatment of Gallbladder Cancer

Inclusion Criteria: * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Patient must have histologically-confirmed T2 or T3 gallbladder cancer discovered incidentally at the time of or following routine cholecystectomy for presumed benign disease * NOTE: Patients with histologically-confirmed Tis, T1a, T1b, or T4 tumors are not eligible * Patient must have undergone initial cholecystectomy within 12 weeks prior to randomization * Patient must have the ability to understand and the willingness to sign a written informed consent document * Leukocytes \>= 3,000/mcL (obtained =\< 28 days prior to randomization) * Absolute neutrophil count \>= 1,500/mcL (obtained =\< 28 days prior to randomization) * Platelets \>= 100,000/mcL (obtained =\< 28 days prior to randomization) * Total bilirubin =\< institutional upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome are eligible if direct bilirubin \< 1.5 x ULN of the direct bilirubin (obtained =\< 28 days prior to randomization) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN (obtained =\< 28 days prior to randomization) * Serum creatinine =\< institutional ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 (Based on Cockcroft Gault estimation) (obtained =\< 28 days prior to randomization) * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of randomization are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association functional classification. To be eligible for this trial, patients should be class 2B or better Exclusion Criteria: * Patient must not have any evidence of metastatic disease or inoperable loco-regional disease based on high-quality, preoperative, cross-sectional imaging (computed tomography \[CT\] or magnetic resonance imaging \[MRI\]) of the chest, abdomen, and pelvis (C/A/P) obtained within 6 weeks prior to randomization, defined as * No radiographic evidence of distant disease (M1 disease) * No radiographic evidence of tumor invasion into multiple extrahepatic organs (T4 disease) * No radiographic evidence of distant lymph node involvement (celiac, para-aortic, para-caval lymph nodes) * No evidence of new-onset ascites * Soft tissue thickening within or in direct communication with the gallbladder fossa, peri-portal lymph node involvement, involvement of one extrahepatic organ, and other disease within the confines of what constitutes 'localized resectable' disease are allowable * Women must not be pregnant or breast feeding due to the potential harm to unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used. All females of child bearing potential must have a serum or urine pregnancy test to rule out pregnancy within 14 days prior to randomization. A female of childbearing potential is defined as any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Women of childbearing potential and sexually active males must not expect to conceive or father children by being strongly advised to use accepted and effective method(s) of contraception or to abstain from sexual intercourse for the duration of their participation in the study