Sorafenib in Treating Patients With Relapsed Chronic Lymphocytic Leukemia

Inclusion Criteria: * Histologically or cytologically confirmed chronic lymphocytic leukemia (CLL) by NCI-WG immunophenotype and blood criteria * Documentation of current or prior peripheral blood (PB) or bone marrow (BM) immunophenotype compatible with CLL * Patients who currently do not have \> 5,000/mm³ absolute lymphocytosis are eligible if they have previously met PB lymphocytosis criteria and have a current immunophenotype documenting monoclonal B lymphocytosis morphologically and immunophenotypically compatible with CLL * Intermediate-risk (Rai stage I or II) or high-risk (Rai stage III or IV) disease, including any of the following: * Rai stage I disease with lymphocytosis and enlarged nodes * Rai stage II disease with lymphocytosis plus splenomegaly and/or hepatomegaly (nodes positive or negative) * Rai stage III disease with lymphocytosis plus anemia * Rai stage IV disease with lymphocytosis and thrombocytopenia * Must require treatment with active disease, experiencing disease related symptoms, or having deterioration of blood counts, meeting ≥ 1 of the following criteria: * Presence of ≥ 1 of the following disease-related symptoms: * Weight loss \> 10% within the past 6 months * Extreme fatigue (i.e., ECOG performance status 2: cannot work or unable to perform usual activities) * Fever \> 100.5°F for 2 weeks without evidence of infection * Night sweats without evidence of infection * Evidence of progressive marrow failure, as manifested by worsening of anemia (hemoglobin \< 10 g/dL), thrombocytopenia (platelet count \< 100,000/mm³), and/or neutropenia (neutrophil count \< 2,000/mm³) * Massive (i.e., \> 6 cm below left costal margin) or progressive splenomegaly or discomfort from splenomegaly * Massive nodes or clusters (i.e., \> 10 cm in longest diameter), progressive adenopathy, or discomfort from lymphadenopathy * Deterioration of blood counts and/or progressive lymphocytosis, with an increase of ≥ 10% documented over a 2-month period OR an anticipated doubling time \< 6 months * Relapsed disease * Must receive at least 1, but no more than 3, prior chemotherapy regimens with any cytotoxic agent or antibody therapy * No fludarabine refractory disease * Responded to prior fludarabine without relapse or disease progression for at least 6 months * Patients with a history of Coombs-positive hemolytic anemia are eligible provided recovery from treatment of hemolysis and off steroids * No stage 0 CLL * No known CNS involvement * Life expectancy \> 6 months * ECOG performance status 0-2 OR Karnofsky performance status 70-100% * Absolute neutrophil count ≥ 1,000/mm³ * Platelets ≥ 30,000/mm³ * Bilirubin ≤ 2 mg/dL * AST/ALT ≤ 2.5 times upper limit of normal (ULN) * Creatinine ≤ 1.5 times ULN OR creatinine clearance ≥ 60 mL/min (for patients with creatinine levels above normal) * No currently active second malignancy * Not pregnant or nursing * Negative pregnancy test * Fertile patient must use effective contraception prior to and during study participation * No uncontrolled hypertension, defined as blood pressure (BP) \> 150/100 mm Hg on 2 different measurements at least 1 day apart with either systolic or diastolic number meeting this definition * Patients may later enter the study, if they have achieved stable BP (i.e., \< 140/90 mm Hg) on a regimen of ≤ 2 drugs after 6-8 weeks of therapy * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib * No uncontrolled intercurrent illness including, but not limited to, any of the following: * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situations that would limit compliance with the study requirements * No active infection requiring systemic antibiotics * No evidence of bleeding diathesis * No evidence of bowel perforation or obstruction risk * No swallowing dysfunction leading to difficulty taking the study drug * See Disease Characteristics * Recovered from prior therapy * At least 2 weeks since prior antibiotic therapy * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) or radiotherapy * At least 12 weeks since prior monoclonal antibody * Concurrent warfarin for anticoagulation allowed provided all of the following are met: * On a stable therapeutic dose * INR ≤ 3 * No active bleeding or pathological condition that carries high-risk of bleeding * No prior MAPK signaling inhibitor agents or anti-angiogenesis agents * No concurrent combination anti-retroviral therapy for HIV-positive patients * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin, or Hypericum perforatum (St. John's wort) * No other concurrent investigational agents