Everolimus and Bendamustine Hydrochloride in Treating Patients With Relapsed or Refractory Hematologic Cancer

Inclusion Criteria: * Measurable disease * Baseline hemoglobin level of \> 7.0 g/dl * Understand and voluntarily sign an informed consent form * Able to adhere to the study visit schedule and other protocol requirements * All the patients need to have biopsy proven active disease at the time of clinical trial * Eastern Cooperative Oncology Group performance status of =\< 2 study entry * Absolute neutrophil count \>= 1,000/mm\^3 * Platelet count \>= 50,000/mm\^3 * Calculated creatinine clearance \> 40 ml/min or 24 hour urine * Total bilirubin =\< 2 x upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x upper limit of normal * International normalized ratio \< 2 Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form * Currently part of or have participated in any clinical investigation with an investigational drug within 1 month prior to dosing * Any severe and/or uncontrolled medical conditions * Uncontrolled diabetes mellitus * Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral everolimus * Currently receiving anticancer therapies or who have received anticancer therapies within 2 weeks of the start of everolimus * Known hypersensitivity to everolimus or bendamustine * Known central nervous system (CNS) disease (NHL, diffuse large B cell lymphoma \[DLBCL\]) * Recent major surgery within 14 days prior to cycle 1, day 1 * Taking strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors * Received live attenuated vaccines * Known sero-positive for active or past viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV); patients who are sero-positive because of hepatitis B virus vaccine are eligible * History of another primary malignancy * History of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study * Pregnant or nursing (lactating) women * Women of childbearing potential * Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to randomization; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential * Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 8 weeks after the end of treatment