Bexarotene in Preventing Breast Cancer in Patients at High Risk for Breast Cancer

Inclusion Criteria: * Participants must be at high risk as defined by a history of breast cancer (invasive or ductal breast carcinoma in situ \[DCIS\]) and be at least 5 years out from diagnosis, or lobular carcinoma in situ (LCIS), or proliferative benign breast disease such atypical ductal hyperplasia (ADH), atypical lobular hyperplasia (ALH) or genetic test confirmation of BRCA 1/2 mutation carrier or have a breast cancer risk assessment \>= 1.7% in 5 years or a lifetime risk \>= 20% * No evidence of disease (in situ or invasive cancer that would normally be treated by resection) at trial entry as determined by the investigator; diagnosis of invasive cancer must be at least 5 years prior to initiation on trial * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/microliter * Absolute neutrophil count \>= 1,500/microliter * Platelets \>= 100,000/microliter * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal (ULN) * Creatinine =\< 1.5 x institutional ULN * Hemoglobin \>= 10 g/dL * Thyroid-stimulating hormone (TSH) within normal institutional limits * Triglycerides =\< 300 mg/dl * Total cholesterol =\< 300 mg/dl * \>= 6 months from all previous breast cancer treatment (including endocrine therapy) * Participants must have adequate accessible breast tissue as determined by the treating physician, consisting of one breast unaffected by invasive cancer, which has not been radiated; a history of benign core biopsy of this breast will be permitted * Participants need to have had any breast imaging with a normal/benign (bi-rads 1 or 2) result within 180 days of day 0 and no further routine breast imaging planned during the course of the study (4 weeks); exception: if the mammogram result was a bi-rads 0 and the imaging work-up (ultrasound and/or magnetic resonance imaging \[MRI\]) result comes back normal/benign (bi-rads 1 or 2) before treatment initiation, then participant is eligible. * For women of childbearing potential; negative pregnancy testing within 72 hours prior to or on study visit #1 (day 0) and willingness to use adequate contraception during the study intervention; OR post-menopausal defined as any one of the following 1) prior hysterectomy, 2) absence of menstrual period for 1 year in the absence of prior chemotherapy or 3) absence of menstrual period for 2 years in women with a prior history of chemotherapy exposure who were pre-menopausal prior to chemotherapy; in women of childbearing potential, effective contraception must be used for one month prior to the initiation of therapy, during therapy, and for at least one month following discontinuation of therapy; it is recommended that two reliable forms of contraception be used simultaneously; if participants are interested in enrolling and have not met the requirement for contraception, they will be seen in the clinic in 1 month for re-evaluation once they have met this requirement and ensure all other eligibility criteria is met prior to dose assignment * Willingness to comply with all study interventions and follow-up procedures including the ability to apply the study drug to the breast * Ability to understand and the willingness to sign a written informed consent document * Ability to avoid exposure of the treated breast area to sunlight and artificial ultraviolet light during the use of bexarotene gel Exclusion Criteria: * History of allergic reactions attributed to compounds of similar chemical or biologic composition to bexarotene gel, oral or topical retinoids * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, thromboembolic disease, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant, or had given birth, or nursed at any time during the last 12 months * Women with a history of any cancer within the last 3 years, except for non-melanoma skin cancer; history of breast cancer must be at least \> 5 years from diagnosis * Prior bilateral breast surgery (mastectomy, segmental mastectomy, or breast augmentation surgery including breast implants or breast reductions) or combination of breast radiation and surgery involving both breasts * Prior history or evidence of metastatic breast cancer * Prior history of histologically confirmed bilateral invasive breast cancer * Current use or \< 6 months since use of selective estrogen receptor modulator (SERMS) or aromatase inhibitors or any other investigational treatment for breast cancer prevention or therapy * Skin lesions that disrupt the stratum corneum (e.g., eczema, ulceration) or any breakdown of the skin * Current use of a retinol containing agent or any retinoid analogue drug within the last 30 days * Dietary vitamin A intake \>= 5,000 IU/day (as determined by dietary supplementation) * Treatment with any investigational drug or investigational biologic within 30 days of initiating study treatment or during the study * History of human immunodeficiency virus (HIV) or active hepatitis C