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…