Cyclosporine, Pravastatin Sodium, Etoposide, and Mitoxantrone Hydrochloride in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Treatment-related mortality (TRM) score =\< 9.2 as calculated with simplified model * Prior morphological diagnosis of AML according to the 2008 World Health Organization (WHO) diagnostic criteria; patients with biphenotypic AML are eligible; patients with acute promyelocytic leukemia with t(15;17)(q22;q12) and variants are ineligible * Relapsed/persistent disease as defined by International Working Group criteria; outside diagnostic material is acceptable as long as peripheral blood and/or bone marrow slides are reviewed at the study institution; flow cytometric analysis of peripheral blood and/or bone marrow should be performed according to institutional practice guidelines * Patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) are eligible if relapse occurs \> 180 days post-transplant provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agents * Eastern Cooperative Oncology Group (ECOG) performance status of 0-3, assessed at time of registration * Should be off any active therapy for AML with the exception of hydroxyurea or low-dose cytarabine (=\< 100 mg/m\^2) for at least 14 days prior to study registration unless patient has rapidly progressive disease, and all Grade 2-4 non-hematologic toxicities must have resolved * Bilirubin =\< 2 x Institutional Upper Limit of Normal (IULN) unless elevation is thought to be due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis (assessed within 7 days prior to registration) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamic pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2 x IULN unless elevation is thought to be due to hepatic infiltration by AML (assessed within 7 days prior to registration) * Serum creatinine =\< 1.5 x IULN (assessed within 7 days prior to registration) * Left ventricular ejection fraction \>= 40%, assessed within 28 days prior to registration, e.g. by multi gated acquisition scan (MUGA) scan or echocardiography, or other appropriate diagnostic modality, and no clinical evidence of congestive heart failure; if the patient had anthracycline-based therapy since the most recent cardiac assessment, cardiac evaluation should be repeated if there is clinical or radiographical suspicion of cardiac dysfunction, or if the previous cardiac assessment was abnormal * Patients with symptoms/signs of hyperleukocytosis or white blood cell (WBC) \> 100,000/uL can be treated with leukapheresis prior to enrollment * 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 * Ability to understand and the willingness to sign a written informed consent document; the consent can be obtained from a legally authorized representative if the patient is unable to provide informed consent Exclusion Criteria: * Diagnosis of another malignancy, unless the patient was diagnosed at least 2 years earlier and has been disease-free for at least 6 months following the completion of curative intent therapy with the following exceptions: * Patients with treated non-melanoma skin cancer, in situ carcinoma, or cervical intraepithelial neoplasia, regardless of the disease-free duration, are eligible for this study if definitive treatment for the condition has been completed * Patients with organ-confined prostate cancer with no evidence of recurrent or progressive disease based on prostate-specific antigen (PSA) values are also eligible for this study if hormonal therapy has been initiated or a radical prostatectomy has been performed * Refractory/relapsing blast crisis of chronic myelogenous leukemia (CML) * Known hypersensitivity to any study drug * Human immunodeficiency virus (HIV)-positive patients are excluded if their cluster of differentiation (CD)4 count is below 200 cells/uL or if they have active acquired immune deficiency syndrome (AIDS)-related complications, as these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy * Pregnancy or lactation; women of childbearing potential must undergo pregnancy test within 7 days prior to registration * Uncontrolled systemic fungal, bacterial, viral, or other infection (defined as exhibiting progressive signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment) * Patients may not be receiving any other investigational agents