Sorafenib and Fulvestrant in Treating Patients With Locally Advanced or Metastatic Breast Cancer That Did Not Respond to Aromatase Inhibitor Therapy

Inclusion criteria

DISEASE CHARACTERISTICS: * Diagnosis of incurable breast cancer * Locally advanced or metastatic disease * Measurable or evaluable disease * Measurable disease is defined as ≥ 1 uni-dimensionally measurable lesion ≥ 20 mm by conventional techniques or ≥ 10 mm by spiral computed tomography(CT) scan * Bone-only metastases that can be imaged with bone scan AND magnetic resonance imaging (MRI) or bone scan AND plain x-ray is considered measurable disease * Tumor lesions that are situated in a previously irradiated area are considered measurable only if they are progressing at the time of study entry * Evaluable disease includes unresectable skin/chest wall metastases that can be photographed and whose size can be measured with a ruler * Bone-only metastases that can only be imaged using bone scan or malignant pleural effusion(s) only are not considered evaluable disease * Previously treated with a third-generation aromatase inhibitor (e.g., letrozole, anastrazole, or exemestane) AND meets one of the following criteria: * Progressed during palliative aromatase inhibitor therapy * Recurred during adjuvant aromatase inhibitor therapy * Recurred within 12 months of completing adjuvant aromatase inhibitor therapy * Human Epidermal growth factor Receptor 2(HER2/neu)-negative tumor * No Human Epidermal growth factor Receptor 2(HER2/neu) overexpression (i.e., tumor staining 3+ by immunohistochemistry \[IHC\] or gene amplified by Fluorescence In Situ Hybridization \[FISH\]) * Hormone receptor status: * Estrogen receptor and/or progesterone receptor positive, defined as ≥ 10% of malignant cells with positive nuclear staining PATIENT CHARACTERISTICS: * Postmenopausal * Eastern Cooperative Group(ECOG) performance status 0-1 * Life expectancy ≥ 16 weeks * Neutrophil count ≥ 1,500/mm\^³ * Platelet count ≥ 100,000/mm\^³ * Hemoglobin ≥ 9.0 g/dL * Creatinine \< 2 mg/dL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase(AST) ≤ 2.5 times ULN (≤ 5 times ULN for patients with liver involvement) * International Normalized Ratio(INR) \< 1.5 OR Prothrombin time/ partial thromboplastin time (PT/PTT) normal * Left ventricular ejection fraction(LVEF) normal by Multiple Gated Acquisition(MUGA) or ECHO * No known allergy to sorafenib tosylate or fulvestrant * No cardiac disease, including any of the following: * New York Heart Association(NYHA) class III-IV congestive heart failure * Unstable angina (anginal symptoms at rest) or new-onset angina (within the past 3 months) * Myocardial infarction within the past 6 months * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * No uncontrolled hypertension, defined as systolic blood pressure \> 150 mm Hg or diastolic blood pressure \> 90 mm Hg despite optimal medical management * No thrombotic or embolic events, such as cerebrovascular accident (including transient ischemic attacks), within the past 6 months * No known HIV infection or chronic hepatitis B or C infection * No infection that requires IV antibiotics or produces a fever \> 100°F within the past 72 hours * No pulmonary hemorrhage/bleeding event ≥ Common terminology criteria for adverse events(CTCAE) grade 2 within the past 4 weeks * No other hemorrhage/bleeding event ≥ CTCAE grade 3 within the past 4 weeks * No evidence or history of bleeding diathesis or coagulopathy * No significant traumatic injury within the past 2 weeks * No serious, nonhealing wound, ulcer, or bone fracture * No condition that impairs the patient's ability to swallow whole pills * No malabsorption problem * No second malignancy within the past 5 years, except adequately treated and cured basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * No underlying medical condition that, in the principal investigator's opinion, will make the administration of study drug hazardous or would obscure the interpretation of adverse events PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior chemotherapy for metastatic or unresectable locally advanced breast cancer * No prior sorafenib tosylate or other Vascular endothelial growth factor(VEGF)-targeting therapies * More than 2 weeks since prior major surgery or open biopsy * No concurrent anticoagulation with warfarin or heparin * No concurrent Hypericum perforatum (St. John wort) or rifampin * No other concurrent anticancer agents, including chemotherapy or biological therapy * No other concurrent investigational drugs * Concurrent bisphosphonates allowed