Apolizumab in Treating Patients With Relapsed or Refractory Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria:

* Histologically confirmed hematologic malignancy of 1 of the following histologies:

  * Chronic lymphocytic leukemia (CLL)
  * Small lymphocytic lymphoma (SLL)

    * Noncontiguous stage II or stage III or IV disease
* Received \>= 1 form of prior immunotherapy or chemotherapy

  * Completed therapy at least 4 weeks ago
* Requires therapy (unless early bone marrow transplantation is planned), as indicated by 1 of the following criteria:

  * Progressively worsening disease (symptoms increasing in severity by 1 toxicity criterion over a period of \>= 2 weeks)
  * Progressively worsening anemia or thrombocytopenia
  * Progressively worsening lymphadenopathy
  * Massive splenomegaly or hypersplenism
  * Hyperlymphocytosis (WBC \> 200,000/mm\^3) OR lymphocyte doubling time \< 12 months
  * Marrow failure due to marrow infiltration by leukemia or lymphoma
* Leukemia cells must express 1D10 antigen \> 2 times mean fluorescent intensity of the control by flow cytometry of blood or bone marrow cells
* Performance status - ECOG 0-2
* At least 2 years
* Platelet count \>= 50,000/mm\^3 (transfusion independent)
* Bilirubin =\< 3 mg/dL (unless due to tumor involvement)
* Creatinine =\< 2.0 mg/dL
* No decompensated congestive heart failure
* No unstable angina
* No myocardial infarction within the past 6 months not corrected by surgery or percutaneous transluminal coronary angioplasty
* No active infection requiring oral or IV antibiotics
* No other malignancy that limits life expectancy to \< 2 years or that requires active anticancer therapy within 4 weeks of study entry
* HIV negative
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception during and for at least 3 months after study treatment
* Recovered from prior immunotherapy
* More than 3 months since prior alemtuzumab or rituximab
* No prior apolizumab
* Recovered from prior chemotherapy
* More than 4 weeks since prior anticancer hormonal therapy
* More than 4 weeks since prior anticancer radiotherapy
* More than 4 weeks since prior anticancer surgery
* At least 4 weeks since other prior therapy for CLL or SLL and recovered