Estradiol in Treating Patients With ER Beta Positive, Triple Negative Locally Advanced or Metastatic Breast Cancer

Inclusion Criteria: * PRE-SCREENING CRITERIA (STEP 0): Women of age \>= 18 years * PRE-SCREENING CRITERIA (STEP 0): History of locally advanced or metastatic breast cancer that is ERalpha negative or low (\< 1% nuclear staining) and HER2 negative. * Note: HER2 negative disease per 2018 American Society of Clinical Oncology/College of American of Pathologists (ASCO/CAP) guidelines, one of the following must apply: * 0 or 1+ by immunohistochemistry (IHC) and not amplified by in situ hybridization (ISH); * 0 or 1+ by IHC and ISH not done; * 2+ by IHC and ISH results are: \< 6.0 HER2 signals/cell with HER2/CEP17 ratio \< 2.0; * IHC not done and not amplified by ISH. * PRE-SCREENING CRITERIA (STEP 0): =\< 3 prior chemotherapy regimens for treatment of metastatic breast cancer. * Note: Prior use of monoclonal antibodies targeting PD1, PDL1 is allowed (if administered as monotherapy it is not counted as a chemotherapy regimen). * PRE-SCREENING CRITERIA (STEP 0): Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * PRE-SCREENING CRITERIA (STEP 0): Willing to submit a biopsy specimen from locally recurrent or metastatic site (or primary if metastatic site not available) of breast cancer for ERbeta staining to Mayo Clinic Anatomic Pathology. * PRE-SCREENING CRITERIA (STEP 0): No prior history of metastatic ERalpha positive breast cancer (\>= 1%) * PRE-REGISTRATION CRITERIA (STEP 1): Presence of moderate or strong nuclear ERbeta staining in \> 25% of cells in specimen submitted during Pre-Screening Step. * PRE-REGISTRATION CRITERIA (STEP 1): For patients who did not have a biopsy or lacking ERalpha, progesterone receptor (PR), and HER2 results from a locally advanced or metastatic site performed =\< 12 months prior to Pre-Registration: Willing to undergo a standard of care biopsy of locally recurrent or metastatic breast cancer for ERalpha, PR, and HER2 as well as additional research cores. * PRE-REGISTRATION CRITERIA (STEP 1): Measurable or non-measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria that will be assessed using imaging-based evaluations. * Note: The tumor lesion biopsied during the pre-registration period is not considered measurable disease nor a target lesion. * PRE-REGISTRATION CRITERIA (STEP 1): If history of brain metastases must meet the following criteria: * Patients with a history of brain metastases are eligible only if they are asymptomatic and have stable disease for \>= 3 months, including \< 28 days of prior to pre-registration. * Not receiving steroids for brain metastases. * PRE-REGISTRATION CRITERIA (STEP 1): ECOG performance status 0 or 1. * PRE-REGISTRATION CRITERIA (STEP 1): =\< 3 prior chemotherapy regimens for treatment of metastatic breast cancer. * NOTE: Prior use of monoclonal antibodies targeting PD1, PDL1 is allowed. * PRE-REGISTRATION CRITERIA (STEP 1): Women must be postmenopausal. * NOTE: Postmenopausal status is verified by: * Prior bilateral surgical oophorectomy, or * Age \>= 60 years, or * Age \< 60 years with no menses for \> 1 year with estradiol levels within postmenopausal range, according to institutional standard. * PRE-REGISTRATION CRITERIA (STEP 1): Able to swallow oral medications. * PRE-REGISTRATION CRITERIA (STEP 1): Willingness to stop use of strong inducers or inhibitors of CYP3A4 prior to registration. * NOTE: Use of strong inducers or inhibitors is allowed during pre-registration as long as patient will complete course prior to registration. * REGISTRATION CRITERIA (STEP 2): For patents who had a biopsy taken from a metastatic site =\< 12 months prior to Pre-Registration: Confirmation from the local lab that the tumor from this biopsy was ERalpha negative (\< 1% nuclear staining) and HER2 negative * REGISTRATION CRITERIA (STEP 2): For patients who underwent a pre-registration biopsy: Histologic confirmation from local lab that tumor is ERalpha negative (\< 1% nuclear staining), and HER2 negative * REGISTRATION CRITERIA (STEP 2): Hemoglobin \>= 8 g/dL (=\< 14 days prior to registration). * REGISTRATION CRITERIA (STEP 2): Platelet count \>= 75,000/mm\^3 (=\< 14 days prior to registration). * REGISTRATION CRITERIA (STEP 2): Creatinine =\< 1.5 x upper limit of normal (ULN) (=\< 14 days prior to registration). * REGISTRATION CRITERIA (STEP 2): Total bilirubin =\< 1.5 x ULN (=\< 14 days prior to registration). * REGISTRATION CRITERIA (STEP 2): Aspartate aminotransferase/serum glutamic-oxaloacetic transaminase (AST/SGOT) =\< 2.5 x ULN (=\< 14 days prior to registration). * For patients with liver metastasis =\< 5 x ULN. Exclusion Criteria: * PRE-REGISTRATION CRITERIA: Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection. * Symptomatic congestive heart failure. * Unstable angina pectoris. * Uncontrolled symptomatic cardiac arrhythmia. * Uncontrolled hypertension (defined as blood pressure \> 160/90). * PRE-REGISTRATION CRITERIA: Deep vein thrombosis / pulmonary embolism (DVT/PE) =\< 12 months prior to pre-registration. * Note: Patients who are on anticoagulant therapy for maintenance are eligible as long as the DVT and/or PE occurred \> 6 months prior to pre-registration, and there is no evidence for active thrombosis (either DVT or PE). * PRE-REGISTRATION CRITERIA: Stroke =\< 6 months prior to pre-registration. * PRE-REGISTRATION CRITERIA: Two or more episodes of DVT and/or PE =\< 5 years prior to pre-registration. * PRE-REGISTRATION CRITERIA: Abnormal uterine bleeding =\< 6 months prior to pre-registration * PRE-REGISTRATION CRITERIA: History of coagulopathy. * PRE-REGISTRATION CRITERIA: Other active second malignancy other than non-melanoma skin cancers within 3 years prior to pre-registration. * NOTE: A second malignancy is not considered active if all treatment for that malignancy is completed and the patient has been disease-free for \>= 3 years prior to pre-registration. * REGISTRATION CRITERIA: None of the following therapies are allowed =\< 14 days prior to registration. * Chemotherapy. * Immunotherapy. * Biologic therapy. * Hormonal therapy. * Monoclonal antibodies. * Anti-HER2 or other "targeted" (e.g. mTOR) therapy. * Note: Any adverse events derived from these therapies must be =\< grade 2 prior to starting study therapy (exceptions for alopecia).