Alvespimycin Hydrochloride in Treating Patients With Relapsed Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or B-Cell Prolymphocytic Leukemia

Inclusion Criteria: * Patients must have histologically confirmed B-CLL/SLL or a B-PLL according to 2008 World Health Organization (WHO) diagnostic criteria * Patients must meet one or more of the following modified indications for treatment as described in the 2008 International Workshop on CLL (IWCLL) guidelines for the diagnosis and treatment of CLL: * Progressive disease, marked splenomegaly, and/or lymphadenopathy, or need to de-bulk disease for future allogeneic transplantation * Anemia (hemoglobin \< 11 g/dL) or thrombocytopenia (platelet count \< 100,000/mm\^3) * Unexplained weight loss exceeding 10% of body weight over the past 6 months * Fatigue grade 2 or 3 as measured by Cancer Therapy Evaluation Program (CTEP) Active Version * Fevers \> 100.5º F OR night sweats for \> 2 weeks without evidence of infection * Progressive lymphocytosis, with an increase exceeding 50% over a 2-month period or a doubling time of \< 6 months * Patients must have received at least one prior therapy that includes either fludarabine or equivalent nucleoside analogue, or an alternative regimen if a contra-indication (i.e. autoimmune hemolytic anemia) or patient desire not to receive fludarabine exists * Children are excluded from this study but may be eligible for future pediatric trials * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional ULN * Creatinine within normal institutional limits * Creatinine clearance \>= 50 mL/min/1.73 for patients with creatinine levels above institutional normal * QTc \< 500 msec * Left ventricular ejection fraction (LVEF) \> 40% by multi gated acquisition scan (MUGA) * No history of serious ventricular arrhythmia * No myocardial infarction or active ischemic heart disease within the past year * No New York Heart Association (NYHA) class III or IV congestive heart failure * No poorly controlled angina * No uncontrolled dysrhythmia requiring medication * No left bundle branch block * No history of congenital long QT syndrome * Pulse oximetry at rest or on exercise \> 88% * No symptomatic pulmonary disease (Asthma or COPD that is controlled is acceptable) * Women of childbearing potential (WOCP) are required to have negative pregnancy test (serum) within 10-14 days and within 24 hours prior to the first dose of 17-DMAG; further, WOCP and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for a time frame of 14 days prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, the treating physician should be notified immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; corticosteroids alone will not be considered prior therapy, but must be discontinued at least 24 hours prior to the first day of 17-DMAG administration unless continued for indications other than the primary malignancy * Patients may not be receiving any other investigational agents * Patients with known central nervous system involvement should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to 17-DMAG * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection requiring iv antibiotics, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because 17-DMAG is an agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with 17-DMAG, breastfeeding should be discontinued if the mother is treated with 17-DMAG * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with 17-DMAG