Low Dose Tamoxifen With or Without Omega-3 Fatty Acids for Breast Cancer Risk Reduction

Inclusion Criteria: * Age 45 - 74 * Postmenopausal female * Postmenopausal is defined as either * Prior removal of the ovaries, or if ovaries intact amenorrhea for \>= 12 months and not on any form of contraception, or * Amenorrhea for greater than 2 months with serum follicle-stimulating hormone (FSH) in postmenopausal range (\>= 25 IU/L). Women with ovaries and a prior hysterectomy or endometrial ablation \< age 55 must have a FSH \>= 25 IU/L. Women may be on vaginal low dose estrogen preparations for vaginal dryness. Women over age 50 with a levonorgestrel intrauterine device in place for 2 or more years and not planning removal in the next 6 month are also eligible if FSH \>= 25 IU/L * Note: FSH will be done at time of screening * Women with intact ovaries and uterus \< age 55 must have a negative pregnancy test prior to randomization * Overweight or obese (body mass index \[BMI\] \>= 25 kg/m\^2) * Note: BMI must be calculated within 28 days of randomization * Willing to undergo a fasting blood draw and non-fasting RPFNA with fixed and frozen aliquots sent to University of Kansas Medical Center (KUMC) * At increased risk of breast cancer per at least one of the following: * Personal medical history * History of atypical hyperplasia or lobular carcinoma in situ (LCIS) found on breast biopsy * History of unilateral ductal carcinoma in situ treated with unilateral mastectomy, lumpectomy, or local excision with or without radiation and this treatment was completed at least 3 months prior to the screening RPFNA * High mammographic density determined by one of the following: * Visual estimate of area of density (VAS) \> 50%, * Volpara (trademark) \>= 15% dense volume (Volpara d) * Breast Imaging Reporting and Data System (BIRADS) assessment = extremely dense (BIRADs D) * Genetic test result * Germline gene mutation in ATM, BARD1, BRCA2, CDH1, CHEK2, NF1, PALB2, PTEN, RAD51C, RAD51D, or STK11 * Polygenic lifetime risk score \>= 2x average or 25% * Calculated risk based on standard models * Five-year Breast Cancer Risk Assessment Tool (BCRAT) (version 2.0) \>= 1.66% * Ten-year International Breast Cancer Intervention Study risk evaluation tool (IBIS) (version 8) \>= 3% * Ten-year relative risk IBIS (version 8) \>= 2X that for age group * Ten- year Breast Cancer Surveillance Consortium (version 2) \>= 3% * Family History * Breast cancer in a first or second degree relative (female or male) with onset under age 50. (First degree relative = parent, sibling, or child. Second degree relative = grandparent, uncle, aunt, nephew, niece, half-sibling, grandchild or first cousin) * Breast cancer in two or more first or second-degree relatives from either the maternal or paternal linage without regard to age * Bilateral breast cancer or breast and ovarian cancer in the same first or second degree relative without regard to age * Primary source documentation of risk is required and must be submitted to the lead academic organization (LAO) for review along with the eligibility checklist * Risk factor: Atypical hyperplasia or LCIS; Primary source document: Copy of pathology report or clinical note confirming the diagnosis * Risk factor: Ductal carcinoma in situ (DCIS) and treatment history; Primary source document: Copies of pathology report or clinic notes confirming the diagnosis, treatment plan and treatment end date(s) * Risk factor: Mammographic density; Primary source document: Copy of clinic note or mammogram report * Risk factor: Genetic; Primary source document: Copy of genetic test report * Risk factor: Calculated based on standard models; Primary source document: Copy of the calculation result * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Note: Higher total bilirubin levels (=\< 3 mg/dL) can be allowed if due to known benign liver condition, i.e., Gilbert's syndrome * Results from prior laboratory testing within 180 days of randomization may be used * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) =\< 3.0 x institutional upper limit of normal * Results from prior laboratory testing within 180 days of randomization may be used * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal * Results from prior laboratory testing within 180 days of randomization may be used * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients on chronic suppressive antiviral therapy for herpes simplex virus (HSV) are eligible * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Women must have at least 1 unaffected untreated breast for fine needle aspiration. Women may have had prior unilateral breast radiation or mastectomy for DCIS * Ability to understand and the willingness to sign a written informed consent document * Most recent screening mammogram must be performed ≤ 12 months prior to RPFNA and must be reported as BIRAD 1 or 2. If BIRAD 0 then follow-up diagnostic imaging must be BIRAD 1 or 2 or cleared clinically with radiology recommendation of return to annual screening * Confirmation that baseline research blood was drawn fasting (\>= 10 hours), has been received in good condition at KUMC, and is archived for assessment of primary endpoint Exclusion Criteria: * Exclusions based on current or past conditions: * Bilateral breast implants (danger of implant puncture with RPFNA) * Prior invasive breast cancer * Prior invasive uterine cancer * Other prior invasive cancer and haven't completed cancer related therapy or with evidence of disease (other than non-melanoma skin cancer) within the past 2 years * Currently breastfeeding (concern that tamoxifen may be in breast milk) or nursing within past 12 months (concern about milk fistula with RPFNA) * Type I or type II diabetes mellitus requiring current pharmacologic treatment (including metformin, glucagon-like peptide 1 agonists, insulin, sulfonylurea) * Prior deep vein thrombosis, pulmonary embolus, or stroke * Prior gastric bypass surgery * History of chronic liver disease including NASH (nonalcoholic steatohepatitis) or cirrhosis * Pathogenic or likely pathogenic germline mutation in BRCA1 or TP53 * Exclusions based on medications: * Current use of prescription anticoagulants such as Coumadin (warfarin), direct-acting oral anticoagulants such as Xarelto (rivaroxaban) or Eliquis (apixaban) or heparin * Women who would not be able to or do not wish to discontinue daily use of aspirin (81mg or higher) and aspirin containing products (81 mg or higher) at least 3 weeks prior to each RPFNA * Note: Women may resume daily use of aspirin and aspirin containing products 3 days after each RPFNA procedure * Current use of a levonorgestrel intrauterine device if in place less than 2 years or if there is planned removal within the next 6 months * Current use of hormone therapy (oral, transdermal, or injectable) * Note: Vaginal estrogen is allowed * Prior treatment with tamoxifen, aromatase inhibitor or selective estrogen receptor degrader for more than 2 months * Note: Women with \< 2 months of these drugs must be off for at least 6 months before they may begin biomarker screening tests * Greater than 1 gram daily of omega-3 fatty acid supplement within the last 6 months * Current use of prescription immunosuppressive drugs * Current use of CYP3A4 strong inducers rifampin or aminoglutethimide * Current use of or plans to initiate a glucagon-like peptide 1 agonist within the next 6 months * Current use of metformin for any indication * Participants may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to tamoxifen or omega-3 fatty acid or generic Lovaza or compounds of similar chemical composition * Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements