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