Bevacizumab in Treating Patients With Relapsed or Refractory Chronic Lymphocytic Leukemia

Inclusion Criteria:

* Diagnosis of B-cell chronic lymphocytic leukemia (CLL)\*, as defined by the following phenotypic characteristics:

  * Predominant population of cells share both B-cell antigens (CD19, CD20, or CD23) as well as the T-cell antigen (CD-5), in the absence of other pan-T-cell markers (CD-3, CD-2, etc.)

    * Mantle cell lymphoma must be excluded by demonstrating the absence of the t(11;14) by fluorescent in situ hybridization (FISH)
  * Dim surface immunoglobulin expression
  * Exclusively kappa and lambda light chains
* Peripheral blood absolute lymphocyte count \> 5,000/mm\^3

  * Lymphocytosis must consist of small to moderate size lymphocytes, with ≤ 55% prolymphocytes, atypical lymphocytes, or lymphoblasts morphologically
* Requires chemotherapy, as indicated by any of the following:

  * Disease related symptoms, including the following:

    * Weight loss ≥ 10% within the previous 6 months
    * Extreme fatigue
    * Fevers \> 100.5°F for 2 weeks without evidence of infection
    * Night sweats without evidence of infection
  * Evidence of progressive marrow failure, as manifested by the development of or worsening anemia (hemoglobin ≤ 10 g/dL) and/or thrombocytopenia (platelet count ≤ 100,000/mm\^3)
  * Massive (i.e., \> 6 cm below left costal margin) or progressive splenomegaly
  * Measurable and progressive lymphadenopathy
  * Measurable (i.e., \> 5,000/mm\^3) and progressive lymphocytosis
* Progressive disease or relapsed after or refractory to 1 course of an alkylating agent-based or purine nucleoside-based (e.g., fludarabine) regimen
* No marrow function attributable to dysplasia related to prior therapy
* ECOG performance status 0, 1, or 2
* Serum creatinine \< 2 mg/dL

  * If serum creatinine \> 1.5 mg/dL but \< 2 mg/dL, creatinine clearance must be ≥ 30 mL/min
* Platelet count \> 30,000/mm\^3
* Direct bilirubin ≤ 2 mg/dL
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No other second malignancy within the past 2 years except squamous cell or basal cell carcinoma of the skin or in situ carcinoma of the cervix
* No New York Heart Association class III or IV heart failure
* No blood pressure \> 150/90 mm Hg
* No unstable angina
* No myocardial infarction or stroke within the past 6 months
* No clinically significant peripheral vascular disease
* No evidence of bleeding diathesis or coagulopathy
* No significant traumatic injury within the past 28 days
* Urine protein:creatinine (UPC) ratio ≤ 1.0

  * Patients with a UPC ratio \> 1.0 must undergo a 23-hour urine collection and must demonstrate \< 1 gram of protein per day
* No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 6 months
* No serious, non-healing wound, ulcer, or bone fracture
* No active infections requiring oral or intravenous antibiotics
* No active bleeding or pathological conditions that carry a high risk of bleeding (e.g., known varices)
* No thrombocytopenia requiring transfusion
* See Disease Characteristics
* More than 4 weeks since prior participation in an experimental drug study
* At least 8 weeks since prior rituximab
* At least 6 weeks since prior chemotherapy
* More than 28 days since prior major surgery or open biopsy
* More than 7 days since prior minor surgery, fine needle aspirations, or core biopsies
* No concurrent major surgery
* No concurrent participation in another experimental drug study
* Concurrent full-dose warfarin or low molecular weight heparin allowed provided patient is on a stable dose AND INR is in range