Sorafenib and Vinorelbine in Treating Women With Stage IV Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed stage IV adenocarcinoma of the breast; (unless metastatic disease is documented by computed tomography \[CT\] scan, magnetic resonance imaging \[MRI\], or bone scan; also, skin disease that has not been biopsied maybe used if in the investigators clinical opinion this represents metastatic disease) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>20 mm with conventional techniques or as \>10 mm with spiral CT scan * Prior adjuvant therapy, and up to 2 lines of prior chemotherapy (including trastuzumab containing regimens in Her-2 positive patients) for metastatic disease are allowed; prior radiation therapy is allowed, prior hormonal therapy is allowed; the total number of patients enrolled with prior trastuzumab containing regimens will not exceed 10; no more than 50% of enrolled patients will receive the study regimen in a third line setting * Life expectancy of greater than 6 months * Performance status: Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0-2 * Hemoglobin \>= 9.0 g/dl * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 times ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 times the upper limit of normal (ULN) (=\< 5 x ULN for patients with liver involvement) * Creatinine =\< 1.5 times ULN * International normalized ratio (INR) \< 1.5 or a prothrombin time (PT)/partial thromboplastin time (PTT) within normal limits; patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate; for patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; women of childbearing potential must have a negative serum pregnancy test performed within 7 days to the start of treatment; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks prior; patients who had bevacizumab within 4 weeks prior to entering the study are allowed * Patients may not be receiving any other investigational agents * Patients with known brain metastases are excluded from this clinical trial; patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (\> Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2), symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, cardiac ventricular arrhythmias requiring anti-arrhythmic therapy, or psychiatric illness/social situations that would limit compliance with study requirements * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management * Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Pulmonary hemorrhage/bleeding event \>= CTCAE Grade 2 within 4 weeks of first dose of study drug * Any other hemorrhage/bleeding event \>= CTCAE Grade 3 within 4 weeks of first dose of study drug * Serious non-healing wound, ulcer, or bone fracture * Evidence or history of bleeding diathesis or coagulopathy * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug * Use of St. John's Wort or rifampin (rifampicin) * Known or suspected allergy to sorafenib or any agent given in the course of this trial * Pregnant women * Human immunodeficiency virus (HIV)-positive patients * Any condition that impairs patient's ability to swallow whole pills * Any malabsorption problem * Patients who received prior sunitinib are excluded