PRIMARY OBJECTIVES: I. Determine the response rate and progression-free survival rate in patients with relapsed or refractory chronic lymphocytic leukemia (CLL) or noncontiguous stage II or stage III or IV small lymphocytic lymphoma treated with apolizumab. II. Determine the safety of this drug, in terms of the frequency and severity of treatment-related adverse events, in these patients. SECONDARY OBJECTIVES: I. Determine clinical response to apolizumab varies by genetic subtype of CLL. II. Determine if pharmacokinetic clearance is truly predicted by 1D10 antigen density on the individual patient CLL cell and how apolizumab clearance correlates with response and selected toxicities observed. III. To determine the importance of reactive oxygen species and specific signaling pathways in promoting apolizumab-mediated apoptosis in vitro and in vivo in primary CLL cells and if this correlates with clinical response to therapy. IV. To determine the cellular properties which convey resistance to apolizumab in CLL in vivo. OUTLINE: This is a multicenter study. Patients receive apolizumab IV over 2-4 hours on days 1, 2, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, and 26 in the absence of disease progression or unacceptable toxicity. Patients are followed at 1 week, at 1 and 2 months, every 3 months for 1 year, and then every 6 months for 3 years.
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
is designated in this study