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 en…