Testing Obeticholic Acid for Familial Adenomatous Polyposis

Inclusion Criteria: * Participants must have a diagnosis of phenotypic FAP with disease involvement of the duodenum and rectum as defined by: * Genetic diagnosis: APC germline mutation (with or without family history) or obligate carrier * Clinical diagnosis: FAP phenotype with \> 100 adenomas in large intestine and participant has a family history of FAP * Clinical diagnosis: FAP phenotype who are status post colectomy for polyposis, participant has a family history of FAP, and 2 FAP experts agree to the diagnosis * Attenuated FAP diagnosis: APC germline mutation required * Participants must have no evidence of active or recurrent invasive cancer for 6 months prior to screening and must be at least 6 months from any prior cancer-directed treatment (such as surgical resection, chemotherapy, immunotherapy, hormonal therapy or radiation) * Age \>= 18 years. Because no dosing or adverse event (AE) data are currently available on the use of OCA in participants \< 18 years of age, children are excluded from this study but will be eligible for future pediatric trials, if applicable * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Hemoglobin \>= 10 g/dL or hematocrit \>= 30% * Leukocyte count \>= 3,500/microliter * Platelet count \>= 100,000/microliter * Absolute neutrophil count \>= 1,500/microliter * Creatinine clearance (calculated if measured is not available) \>= 30 mL/min/1.73m\^2 * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x the institutional upper limit of normal (ULN) * Total bilirubin =\< 1.0 x ULN * Alkaline phosphatase =\< 1.5 x ULN * Gamma-glutamyl transferase (GGT) =\< 1.5 x ULN * Presence of Spigelman stage II or III duodenal polyposis at screening * Presence of intact rectum or ileo-rectal anastomosis (IRA) or ileal pouch-anal anastomosis (IPAA) or end ileostomy * Participants must have a negative test result for human immunodeficiency virus (HIV); if tested within the past 6 months, result will be accepted without repeating the test * Participants must have negative test for hepatitis C virus (HCV) and B virus (HBV) * Willing and able to adhere to the prohibitions and restrictions specified in the final approved protocol * The effects of OCA on the developing human fetus at the recommended therapeutic dose are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, throughout the duration of study participation, and for at least 6 months after receiving the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately * Willingness to moderate alcohol intake (consuming no more than 1 or 2 alcoholic drinks per day for women and men, respectively) * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior use of study drug * Duodenal or rectal/pouch polyp burden that is not quantifiable * Histologically-confirmed high-grade dysplasia or cancer on biopsy at screening * Individuals with active, known or suspected chronic liver disease including cirrhosis, nonalcoholic steatohepatitis (NASH) with liver fibrosis, NASH with cirrhosis, primary sclerosing cholangitis, biliary atresia * Individuals with acute cholecystitis (defined by a syndrome of right upper quadrant pain, fever, and leukocytosis associated with gallbladder inflammation) * Individuals with a history of pancreatitis or presence of pancreatic abnormalities suggestive of increased risk of pancreatitis * Individuals with hepatic steatosis and velocity \> 1.7 meters/second (m/s) as determined by liver ultrasound elastography * Individuals with hyperlipidemia not well controlled with the use of pharmacotherapy and/or dietary modifications * History of severe, progressive, or uncontrolled renal, genitourinary, hepatic, hematologic, endocrine, cardiac, vascular, pulmonary, rheumatologic, neurologic, psychiatric, or metabolic disturbances, or signs and symptoms thereof * Pregnant, breast-feeding, or women of childbearing potential unwilling to use a reliable contraceptive method. Pregnant women are excluded from this study because OCA is an agent with unknown effects on the developing human fetus. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with OCA, breastfeeding should be discontinued if the mother is treated with OCA * Known hypersensitivity, allergies, or intolerance to the study drug or compounds of similar chemical or biologic composition * Any serious and/or unstable pre-existing medical disorder (aside from malignancy exception above), psychiatric disorder, or other conditions that could interfere with participant's safety, obtaining informed consent, or compliance to the study procedures * Participants may not be receiving any other investigational agents * 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 * Individuals with active and untreated hepatitis C virus (HCV) and/or or hepatitis B virus (HBV) infection * Individuals with HIV infection are eligible for participation if: * CD4+ count \>= 300/uL * Viral load is undetectable * Receiving highly active antiretroviral therapy (HAART) without known or suspected drug interactions with OCA * Consultation with the participant's infectious disease specialist may be obtained * Individuals taking the drugs listed below may not be randomized unless they are willing to stop the medications (and possibly change to alternative non-excluded medications to treat the same conditions) no less than 5 half-lives days prior to starting OCA or placebo on this study. Consultation with the participant's primary care provider may be obtained but is not required. The use of the following drugs or drug classes is prohibited during OCA/placebo treatment: * Investigational agents * Bile acid sequestrants (bile acid binding resins): cholestyramine, colestipol, or colesevelam * Bile salt efflux pump (BSEP) inhibitors * Clozapine * Theophylline derivatives * Tizanidine * Warfarin * Hepatotoxic drugs such as amiodarone, sodium valproate, certain herbal/dietary supplements, and long-term doxycycline or tetracycline