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