Decitabine, Doxorubicin, and Cyclophosphamide in Treating Children With Relapsed or Refractory Solid Tumors or Neuroblastoma

Inclusion Criteria: * Histologically confirmed diagnosis of either of the following: * Solid tumor (part A) * No lymphoma * Neuroblastoma (part B) * Original diagnosis may be based on elevated urine vanillylmandelic acid (VMA) and homovanillic acid (HVA) and bone marrow examination * Accessible disease by bone marrow aspirate or tumor biopsy * No laparotomy, thoracotomy, endoscopy, or craniotomy for biopsy * No known curative therapy OR therapy proven to prolong survival with an acceptable quality of life available * No known brain or spinal cord metastases * No CNS tumors * Performance status - Karnofsky 50-100% (patients 11 to 21 years of age) * Performance status - Lansky 50-100% (patients ≤ 10 years of age) * Parts A and B without bone marrow infiltration: * Absolute neutrophil count ≥ 1,000/mm\^3 * Platelet count ≥ 100,000/mm\^3 (transfusion independent) * Part B with bone marrow infiltration (i.e., tumor metastatic to bone marrow with granulocytopenia, anemia, and/or thrombocytopenia): * Absolute neutrophil count ≥ 750/mm\^3 * Platelet count ≥ 50,000/mm\^3 (transfusion independent) * Hemoglobin ≥ 8.0 g/dL (transfusion allowed) * No sickle cell anemia * Bilirubin ≤ 1.5 mg/dL * ALT ≤ 5 times upper limit of normal * No significant hepatic dysfunction that would compromise the tolerability of decitabine or interfere with study procedures or results * Creatinine based on age as follows: * ≤ 0.8 mg/dL (5 years of age and under) * ≤ 1.0 mg/dL (6 to 10 years of age) * ≤ 1.2 mg/dL (11 to 15 years of age) * ≤ 1.5 mg/dL (16 to 21 years of age) * Creatinine clearance or radioisotope glomerular filtration rate ≥ 70 mL/min * No significant renal dysfunction that would compromise the tolerability of decitabine or interfere with study procedures or results * Shortening fraction ≥ 28% by echocardiogram * Ejection fraction of ≥ 45% by MUGA * No significant pulmonary dysfunction that would compromise the tolerability of decitabine or interfere with study procedures or results * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No prior allergic reaction attributed to compounds of similar chemical or biological composition to agents used in this study * No uncontrolled serious infection * No significant end-organ dysfunction that would compromise the tolerability of decitabine or interfere with study procedures or results * Recovered from prior immunotherapy * At least 7 days since prior biologic therapy * More than 1 week since prior growth factor therapy (2 weeks for pegfilgrastim) * More than 2 weeks since prior epoetin alfa * At least 6 months since prior autologous stem cell transplantation * At least 6 months since prior allogeneic bone marrow transplantation * Patients must have full organ recovery and no evidence of graft-versus-host disease * No concurrent immunomodulating agents * No concurrent immunotherapy * No concurrent biologic therapy * No concurrent epoetin alfa * Recovered from prior chemotherapy * More than 2 weeks since prior myelosuppressive chemotherapy (6 weeks for nitrosoureas) * Prior total lifetime cumulative anthracycline dose ≤ 450 mg/m\^2 of doxorubicin or equivalent * No other concurrent chemotherapy * No concurrent hydroxyurea * Recovered from prior radiotherapy * More than 2 weeks since prior local palliative small port radiotherapy * More than 6 months since prior substantial bone marrow irradiation (e.g., cranio-spinal irradiation, total body irradiation, or hemi-pelvic irradiation) * No concurrent radiotherapy * No other concurrent anticancer therapy * No other concurrent investigational agents * Concurrent oral iron supplementation for patients with a known iron deficiency or a microcytic hypochromic anemia allowed