Ixabepilone and Hydroxychloroquine in Treating Patients With Metastatic Breast Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed breast cancer * Histologic or cytologic elements can be established on metastatic tumor aspirate or biopsy * Metastatic disease * Measurable disease according to RECIST criteria * Must have received 2 prior chemotherapy regimens for metastatic breast cancer * Anthracycline-resistant (or treated with minimum cumulative doxorubicin dose of 240 mg/m\^2 or epirubicin dose of 360 mg/m\^2) and taxane-resistant disease * Anthracycline resistance is defined as progression while on therapy or within 6 months in the adjuvant/neoadjuvant setting or 3 months in the metastatic setting * Taxane resistance is defined as progression while on therapy or within 12 months in the adjuvant/neoadjuvant setting or 4 months in the metastatic setting * Hormone receptor status known * No known CNS metastases or previously treated and now stable CNS metastases PATIENT CHARACTERISTICS: * Menopausal status not specified * ECOG performance status 0-2 * ANC ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9 g/dL * Total bilirubin ≤ upper limit of normal (ULN) * If patient has Gilbert's disease, then patient must have isolated hyperbilirubinemia (e.g., no other liver function test abnormality), with maximum bilirubin ≤ 2 times ULN * AST and ALT ≤ 2.5 times ULN, independently of liver metastases * Alkaline phosphatase ≤ 2.5 times ULN * Creatinine ≤ 1.5 times ULN OR calculated creatinine clearance ≥ 60 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other active malignancy * History of basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix within the past 3 years allowed provided patient has been treated with curative intent * History of prior malignancy allowed provided patient has been treated with curative intent and has been disease free \> 3 years * None of the following conditions within the past 6 months: * Myocardial infarction * Stroke * Symptomatic peripheral vascular disease * No unstable angina or NYHA class II-IV congestive heart failure * No history of psoriasis or porphyria * No history of hypersensitivity to 4-aminoquinoline compound * No retinal or visual field changes from prior 4-aminoquinoline-compound use * No history of G6PD deficiency * No GI pathology that would interfere with drug bioavailability * No motor or sensory neuropathy ≥ grade 2 (NCI CTCAE) at study entry * No serious uncontrolled medical disorder or active infection at study entry * No rheumatoid arthritis or systemic lupus erythematosus requiring active treatment * No history of HIV * No history of any condition (social or medical) that, in the opinion of the investigator, might interfere with the patient's ability to comply with the protocol or pose additional or unacceptable risk to the patient PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Prior radiation to tumor sites allowed provided: * Radiation was completed ≥ 3 weeks prior to study treatment * All radiation-related toxicities have resolved to ≤ grade 1 * No more than 3 prior chemotherapy regimens in the metastatic setting * No prior ixabepilone or another epothilone * No concurrent highly active antiretroviral therapy * No other concurrent hydroxychloroquine for treatment or prophylaxis of malaria * No other concurrent anticancer investigational or commercial agents or therapies