Methoxyamine and Fludarabine Phosphate in Treating Patients With Relapsed or Refractory Hematologic Malignancies

Inclusion Criteria: * Subjects must have a histologically confirmed hematologic malignancy that has relapsed or proven refractory (in any time frame) to one or more prior therapies, limited to the following subtypes: * Non-Hodgkin lymphoma (NHL), including cutaneous lymphoma * Hodgkin lymphoma (HL) * Chronic lymphocytic leukemia (CLL) * Chronic myeloid leukemia (CML) * Multiple myeloma * Patients must have progressed through standard curative treatment options in the case of NHL and HL or not be candidates for curative therapy * Patients must have measurable disease, and must meet criteria justifying a need to initiate therapy, criteria for measurable disease and criteria for initiating therapy for purposes of this study are defined as follows: * NHL/HL: measurable disease by radiographic criteria (\>= 1 cm by computed tomography); or any degree of bone marrow involvement with lymphoma by morphologic analysis; or measurable skin involvement according to cutaneous lymphoma response criteria; criteria for initiating therapy include aggressive histology (diffuse large B cell lymphoma, nodal T cell lymphomas, Hodgkin lymphoma) or presence of any of the following: systemic symptoms, bulk \>= 5 cm, \>= 3 nodal sites, marrow compromise remaining within limits of adequate function as defined below, splenomegaly \>= 16 cm, disease-related effusion, risk of local compressive symptoms, or circulating lymphoma cells * CLL: measurable disease requires B lymphocytes equal or greater than 5,000/μL, or lymphadenopathy (\>= 1 cm by computed tomography), or bone marrow involvement of any degree; in addition, patients must have one of the following: Rai stage III (hemoglobin \< 11gm/dL) or IV (platelets \< 100,000/uL) disease, progressive splenomegaly, hepatomegaly or lymphadenopathy, weight loss \> 10% over the preceding 6 month period, grade 2 or 3 fatigue, fevers \> 100.5 or night sweats without evidence for infection, progressive lymphocytosis with an increase of \> 50% over a 2 month period or an anticipated doubling time of \< 6 months * Chronic Myeloid Leukemia: measurable disease requires peripheral or bone marrow evidence of CML by hematologic, cytogenetic, or molecular analysis; any patient meets criteria for initiating therapy who has failed \>= 1 prior treatment with a tyrosine kinase inhibitor (relapsed or refractory) * Multiple myeloma: measurable disease and presence of end-organ damage; measurable disease includes any of the following: abnormal free light chain (FLC) ratio, an M-component in the serum or urine, clonal plasma cells in the bone marrow and/or a documented clonal plasmacytoma; end-organ damage includes any of the following: calcium elevation (\> 11.5 mg/dl), anemia (hemoglobin \< 10 g/dl), bone disease (lytic lesions or osteopenia), or renal involvement (proteinuria or any known nephropathy) as long as Cr \< 1.5 mg/dL * Prior chemotherapy and/or radiation are allowed; at least 3 weeks must have elapsed since prior large-field radiation therapy; patients must have been off previous anti-cancer therapy for at least 3 weeks. Non - hematologic acute treatment related toxicities must have resolved to a grade 2 or less, whereas non hematologic chronic treatment related toxicities must be stable or shown improvement in the 4 weeks preceding enrollment. Because of the nature of the diseases treated in this protocol, hematologic toxicities are not included in this criterion and must meet the eligibility criteria described above. At least 12 weeks must have passed since radioimmunotherapy; prior fludarabine treatment is not restricted * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Life expectancy \> 12 weeks * Absolute neutrophil count \> 750/ul * Platelets \> 50,000/ul * Hemoglobin \> 9.0 g/dl * Total bilirubin \< 1.5 mg/dl * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) \< 2.5 x institutional upper limit of normal * Creatinine \< 1.5 mg/dl and/or creatinine clearance \> 60 mL/min/1.73 m\^2 * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not be receiving any other investigational agents or have received other investigational agents for at least 3 weeks * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant and lactating women are excluded from this study * New York Heart Association (NYHA) classification III or IV heart disease * Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases * Known seizure disorder * Known human immunodeficiency virus (HIV) or chronic hepatitis (B or C) infection * Patients unwilling or unable for any reason (personal, medical, or psychiatric) to comply with the protocol * Patients with known hypersensitivity to fludarabine or a history of purine analog associated autoimmune hemolytic anemia or idiopathic thrombocytopenic purpura