Liposome-encapsulated Daunorubicin-Cytarabine, Fludarabine Phosphate, Cytarabine, and Filgrastim in Treating Younger Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients must have had histologic verification of AML at original diagnosis * Patient must have one of the following: * Recurrent disease with \>= 5% blasts in the bone marrow (M2/M3 bone marrow), with or without extramedullary disease. * Recurrent disease with an absolute blast count greater than 1,000 per microliter in the peripheral blood with or without extramedullary disease * To be eligible for the dose-finding phase: (the dose-finding phase completed in 12/2016) * Relapsed patients * Patients must be in first relapse, and * Patients must not have received prior re-induction therapy * Refractory patients * Patients must not have received more than one attempt at remission induction, which may consist of up to two different therapy courses; Children Oncology Group (COG) AAML1031 de novo therapy including induction I and induction II is an example * Treatment-related AML (t-AML) * Patients must be previously untreated for secondary AML * To be eligible for the phase 2 efficacy phase: * Relapse patients: * Patients must be in first marrow relapse, and * Patients must not have received prior re-induction therapy; donor lymphocyte infusion (DLI) is considered a re-induction attempt * Patients must have the status of CNS1 or CNS2 only, and no clinical signs or neurologic symptoms suggestive of CNS leukemia, such as cranial palsy * Patients must have a performance status corresponding to an Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age; Note: patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, stem cell transplant or radiotherapy prior to entering this study; all prior treatment-related toxicities must have resolved to =\< grade 2 prior to enrollment * Myelosuppressive chemotherapy: must not have received myelosuppressive chemotherapy within 3 weeks of entry onto this study (excluding hydroxyurea) * Cytoreduction with hydroxyurea can be initiated and continued for up to 24 hours prior to the start of CPX-351 * Biologic (anti-neoplastic agent): at least 7 days since the completion of therapy with a biologic agent such as steroids, retinoids; Note: for agents that have known adverse events occurring beyond 7 days after administration (i.e. monoclonal antibodies), this period must be extended beyond the time during which acute adverse events are known to occur * Radiation therapy (RT): \>= 2 weeks for local palliative RT (small port); \>= 6 months must have elapsed if prior craniospinal RT or if \>= 50% radiation of pelvis; \>= 6 weeks must have elapsed if other substantial bone marrow (BM) radiation; Note: patients must have received =\< than 13.6 Gray (Gy) prior radiation to the mediastinum * Stem cell transplant (SCT): no evidence of active graft vs. host disease for at least 4 weeks; for allogeneic SCT patients, \>= 3 months must have elapsed since transplant * Must have received no more than 1 prior autologous or allogeneic stem cell transplant. * Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement * Intrathecal cytotoxic therapy: * No waiting period is required for patients having received intrathecal cytarabine, methotrexate, and/or hydrocortisone * At least 14 days must have elapsed since receiving liposomal cytarabine (DepoCyte) by intrathecal injection * Growth factors: * Patients must not have received growth factors for 7 days prior to CPX-351 * Patients must not have received pegfilgrastim for 14 days prior to CPX-351 * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age 1 to \< 2 years: maximum serum creatinine 0.6 mg/dL (males and females) * Age 2 to \< 6 years: maximum serum creatinine 0.8 mg/dL (males and females) * Age 6 to \< 10 years: maximum serum creatinine 1.0 mg/dL (males and females) * Age 10 to \< 13 years: maximum serum creatinine 1.2 mg/dL (males and females) * Age 13 to \< 16 years: maximum serum creatinine 1.5 mg/dL (males) and 1.4 mg/dL (females) * Age \>= 16 years: maximum serum creatinine 1.7 mg/dL (males) and 1.4 mg/dL (females) * Direct bilirubin \< 1.5 x upper limit of normal (ULN) for age and institution * Serum glutamate pyruvate (SGPT) (alanine aminotransferase \[ALT\]) =\< 3.0 x upper limit of normal (ULN) for age and institution (unless it is related to leukemic involvement) * Shortening fraction of \>= 27% by echocardiogram, or * Ejection fraction of \>= 50% by radionuclide angiogram or echocardiogram * Corrected QT (using Bazett's formula \[QTcB\]) interval \< 500 msecs * Patients with seizure disorder may be enrolled if on anticonvulsants and if seizures are well controlled * Central nervous system (CNS) toxicity =\< grade 2 * Patients with a known history of human immunodeficiency virus (HIV) are eligible, if they meet all of the following conditions: * No history of HIV complications with the exception of cluster of differentiation (CD)4 count \< 200 cells/mm\^3 * No antiretroviral therapy with overlapping toxicity such as myelosuppression * HIV viral loads below the limit of detection * No history of highly active antiretroviral therapy (HAART)-resistant HIV * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met Exclusion Criteria: * Patients who have received \> 450 mg/m\^2 daunorubicin equivalents; patients who relapse after receiving AAML0531/AAML1031 therapy will be eligible for this study, provided they have not received any additional anthracyclines; NOTE: for the purposes of determining eligibility for this protocol, the following cardiotoxicity multipliers will be used to determine daunorubicin equivalents: * Doxorubicin (doxorubicin hydrochloride): 1 * Mitoxantrone: 3 * Idarubicin: 3 * Epirubicin: 0.5 * Patients who are currently receiving another investigational drug * Patients receiving medications for treatment of left ventricular systolic dysfunction * Patients with any of the following diagnoses: * Acute promyelocytic leukemia (APL) * Down syndrome * Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome * Wilson's disease and any other disorder of copper metabolism * Juvenile myelomonocytic leukemia (JMML) * Patients with documented active, uncontrolled infection at the time of study entry * Patients with known active hepatitis B virus (HBV) and hepatitis C virus (HCV) infections * Patients with prior allergy to daunorubicin and/or cytarabine * Female patients who are pregnant are ineligible * Lactating females are not eligible * Female patients of childbearing potential are not eligible unless a negative pregnancy test result has been obtained * Sexually active patients of reproductive potential are not eligible unless they have agreed to use an effective contraceptive method for the duration of their study participation and for 6 months after the last dose of chemotherapy