Acolbifene in Preventing Cancer in Premenopausal Women at High Risk of Breast Cancer

Inclusion Criteria: * Gail risk \>= 1.7% and/or relative risk \>= 3 times that for 5-year age group * Premenopausal * More than 6 months since initiating or discontinuing oral contraceptives * At increased risk for breast cancer, as indicated by \>= 1 of the following risk factors: * BRCA1/2 mutation characterized as deleterious or of uncertain significance * Prior atypical ductal hyperplasia, ductal carcinoma in situ, or lobular carcinoma in situ * Prior random periareolar fine needle aspiration (RPFNA) showing atypical hyperplasia * Family history consistent with hereditary breast cancer, as indicated by 1 of the following criteria: * \>= 4 relatives with breast cancer * \>= 2 relatives diagnosed with breast cancer at ≤ 50 years of age * Breast and ovarian cancer diagnosed in same relative * No suspicion for breast cancer on baseline mammogram performed between days 1-10 of menstrual cycle within 3 months prior to screening baseline RPFNA * Exhibits hyperplasia with or without atypia (Masood score \>= 14) with \>= 500 cells AND Ki-67 positivity \>= 2% by RPFNA performed within 6 months prior to initiation of study drug * Estimated visual mammographic breast density category \>= 5% on mammogram performed within 6 months prior to initiation of study drug * Has regular menstrual cycles (between 21 and 35 days) unless using extended regimen oral contraceptives or a contraceptive device (e.g., Mirena IUD) Values for metabolic profile and blood count within normal limits * Absolute granulocyte count \> 1,000/mm\^3 * Platelets \> 100,000/mm\^3 * Hemoglobin \> 10 g/dL * Bilirubin \< 2.0 mg/dL * AST \< 2 times upper limit of normal (ULN) * Albumin \> 3.0 g/dL * Creatinine \< 1.5 mg/dL * Alkaline phosphatase \< 2 times ULN * Concurrent hormonal contraceptives allowed provided patient remains on the same hormonal regimen from 3 months prior to baseline aspiration until the completion of study treatment * Fertile patients must use effective contraception during and for 3 months after completion of study treatment * Willing to ingest recommended dose of calcium and vitamin D for premenopausal bone health (1,200 mg calcium and 800 IU vitamin D daily) * Negative pregnancy test prior to receiving study agent Exclusion Criteria * pregnant or nursing * nursing within the past 6 months * Known osteoporosis or severe osteopenia (T-score -2 or worse by DEXA) * History of symptomatic endometriosis with pelvic pain, poorly controlled migraines, or hot flashes * History of deep venous thrombosis * History of allergic reactions attributed to compounds of similar chemical or biological composition to the study agent * Other condition or concurrent illness that, in the opinion of the investigator, would make the patient a poor candidate for RPFNA * Less than 1 year since prior use of aromatase inhibitors (e.g., anastrozole, exemestane, or letrozole) or selective estrogen receptor modulators (e.g., tamoxifen citrate, raloxifene, or arzoxifene hydrochloride) * Other concurrent chemopreventive agents * Concurrent anticoagulants * Other concurrent investigational agents * Bilateral breast implants