Ixabepilone in Treating Participants With Significant Residual Disease of HER2/Neu Negative Invasive Breast Cancer After Systemic Therapy

Inclusion Criteria: * Patients with histologic confirmation of invasive HER2/neu-negative breast cancer (immunohistochemistry \[IHC\] 0-1+ or fluorescence in situ hybridization \[FISH\]-negative) that have received complete anthracycline and taxane neoadjuvant systemic therapy and that at the time of surgery are expected to have significant residual disease. Therapy should include at least 4 cycles of an anthracycline-based regimen (adriamycin-cytoxan \[AC\], 5-fluorouracil/adriamycin/intravenous \[IV\] cyclophosphamide \[FAC\], fluorouracil-epirubicin-IV cytoxan \[FEC\]) and 12 weeks of a taxane-based regimen (weekly paclitaxel, every 3-week docetaxel). * Patients who did not complete therapy due to disease progression are eligible. * Patients with bilateral breast cancers are eligible. * Patients should have a Karnofsky performance scale of \>= 70%. * Peripheral granulocyte count of \>= 1500/mm\^3. * Platelet count \>= 100000 mm\^3. * Bilirubin within normal laboratory values. * Alkaline phosphatase may be up to 1.5 x upper limit of normal (ULN) of the institution. * Transaminases (alanine aminotransferase \[ALT\] and aspartate aminotransferase \[AST\]) may be up to 1.5 x upper limit of normal (ULN) of the institution. * Creatinine levels within normal range. * Negative serum pregnancy test for a woman of childbearing potential. * Women of childbearing potential (WOCP) must use a reliable and appropriate contraceptive method during the study and 6 months after chemotherapy…