Patients must be able to receive taxane and/or anthracycline based chemotherapy Patients must have completed standard neoadjuvant or adjuvant taxane and/or anthracycline based chemotherapy prior to randomization; completion of chemotherapy will be determined by the treating oncologist, but should include a minimum of 4 cycles (a cycle of weekly paclitaxel is considered 3 doses); patients must be registered within 42 weeks after the last dose of chemotherapy; patients may have started endocrine therapy at any time after the diagnosis of the current breast cancer Eligible for BCT based on clinical examination, mammography and, if standard practice at a given institution, ultrasound and/or tomogram; women who cannot be appropriately selected for BCT based on these standard imaging studies, and for whom additional imaging is recommended to clarify local disease extent, will not be eligible for this trial; for patients who have neoadjuvant therapy, eligibility for BCT is determined at completion of therapy; repeat mammogram +/- ultrasound (US) will be required at completion of neoadjuvant chemotherapy to determine eligibility for BCT Patient must have completed a minimum of 8 weeks of standard neoadjuvant chemotherapy consisting of an anthracycline and/or taxane-based regimen Patients with prior anthracycline therapy will be excluded Patients with therapy-related AML or MDS should have not received prior cumulative anthracycline (daunorubicin equivalent) lifetime dose > 450 mg/m^2 No prior taxane therapy =< 6 months, except as a radiosensitizer Patients must not have received previous systemic anthracycline (intravesical anthracycline is allowed) Patients must have completed neoadjuvant taxane +/- anthracycline; patients must NOT have received cisplatin or carboplatin or capecitabine as part of their neoadjuvant therapy regimen* NOTE: Patients who received preoperative therapy as part of a clinical trial may enroll* NOTE: Patients that were not able to complete their planned neoadjuvant chemotherapy for any reason (i.e. toxicities, etc.) are eligible to participate as long as no further systemic standard of care therapy is planned by the treating physician Patients must have no prior radiation therapy to >= 25% of the bone marrow for prior systemic anthracycline therapy; prior intravesical anthracycline therapy for non-muscle invasive urothelial carcinoma of the bladder is permitted Patient must have progressed or be refractory to prior anthracycline-containing chemotherapy (e.g. R-CHOP, DA-EPOCH-R, etc) Prior taxane is allowed (as long as the patient is not experiencing grade > 1 neuropathy and had no history of disease progression on a taxane therapy within 3 months prior to study enrollment) Patient must have a lifetime cumulative anthracycline dose of >= 250 mg/m^2 DOXOrubicin equivalent without the protection of dexrazoxane (Zinecard) therapy; the anthracycline dose threshold must be met as part of the treatment of a cancer that was diagnosed at < 22 years of age* Note: Institutional records (e.g., clinic note, treatment summary, chemotherapy roadmap) can be used to document lifetime receipt of anthracycline dose Patient must have previously started induction therapy, which includes vincristine, a corticosteroid, pegaspargase, with or without anthracycline, and/or other standard cytotoxic chemotherapy Patient must have completed a minimum of 8 weeks of standard neoadjuvant chemotherapy consisting of an anthracycline and/or taxane-based regimen