Testing the Addition of Radium Therapy (Radium-223 Dichloride) to the Usual Chemotherapy Treatment (Paclitaxel) for Advanced Breast Cancer That Has Spread to the Bones

Inclusion Criteria: * Women or men with metastatic breast cancer with two or more bone metastases identified by technetium Tc-99m (99mTc) bone scintigraphy and/or CT, at least one of these bone lesions must not have been treated with prior radiation therapy * A diagnosis of breast cancer must have been histologically or cytologically confirmed at any time point * Patients with non-bone metastases (in addition to bone metastases) are permitted if: * Five or less visceral metastasis (=\< 4 cm in size) and asymptomatic (not including lymph nodes) * Enlarged lymph nodes =\< 4 cm * Patients with HER2 negative disease (HER2 negativity by immunohistochemistry \[IHC\] or fluorescent in situ hybridization \[FISH\] ratio according to the American Society of Clinical Oncology-College of American Pathologists guideline criteria) (Hammond et al., 2010; Wolff et al., 2013). Hormone-receptor positive (estrogen receptor \[ER\]-positive and/or progesterone receptor \[PR\]-positive) as well as triple-negative (ER-negative, PR-negative and no overexpression of HER2) breast cancer may be enrolled. Hormone receptor status will be determined at the local institution. ER and PR negativity will be defined as \< 1% tumor staining by IHC * Patient must be eligible to receive therapy with paclitaxel for the treatment of their breast cancer. Patients with hormone-receptor positive disease should have progressed on at least one prior line of hormone therapy and a CDK4/6 inhibitor in the metastatic …