Ursodiol in Treating Patients With Barrett Esophagus and Low-Grade Dysplasia

Inclusion Criteria: * Diagnosis of Barrett's esophagus with histologically-confirmed intestinal metaplasia anywhere in the tubular esophagus either with \>= 2 cm of involvement or with a minimum circumferential Barrett's esophagus (BE) length of 1 cm * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 2.0 mg/dL * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2 X institutional upper limit of normal (ULN) * Creatinine =\< 1X ULN * Women of child-bearing potential (i.e., not surgically sterile or less than one year since last menstrual period) agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; women of childbearing potential must have a negative urine pregnancy test within 14 days prior to study agent administration; male subjects must agree to use adequate contraception (barrier method, abstinence, subject has had vasectomy or partner is using effective birth control or is postmenopausal) * Ability to understand and the willingness to sign a written informed consent document * Agree to refrain from any non-steroidal anti-inflammatory drug (NSAID) with the exception of low-dose aspirin (81 mg once daily \[QD\]) during the entire study period * Agree not to take aluminum-containing antacids and anion exchange resins such as cholestyramine, colestimide or colestipol within 2 hours of taking UDCA Exclusion Criteria: * Barrett's esophagus with high grade dysplasia or carcinoma at enrollment * Medical conditions which would make completing endoscopies or completing the trial difficult including but not limited to previous transient ischemic attacks or cerebral vascular disease, severe respiratory disease, severe ischemic heart disease or myocardial infarction in the previous 6 months, inflammatory bowel disease * Participants may not be receiving any other investigational agents within 1 month of study enrollment * Have used NSAID for more than 5 days per month within 1 month of enrollment except low dose aspirin (81 mg QD) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to UDCA * 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 * Pregnant and breastfeeding women are excluded from this study; breastfeeding should be discontinued during treatment; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately * Have had major upper gastrointestinal (GI) surgeries within 6 months of enrollment including, but not limited to, fundoplication, bariatric surgery, cholecystectomy * Erosive esophagitis detected at the baseline endoscopy * Participants who need concurrent chemotherapy, radiotherapy, or cancer-related hormonal or immunotherapy during the time of study * Participants who have had chemotherapy, radiotherapy, or cancer-related hormonal or immunotherapy within 18 months of the baseline visit * Current or planned use of anticoagulant drugs including, but not limited to, warfarin, heparin, low molecular weight heparin, Plavix, or Aggrenox * Use of cyclosporine during the time of study