Trebananib in Treating Younger Patients With Relapsed or Refractory Solid Tumors, Including Central Nervous System Tumors

Inclusion Criteria: * Part 1: Patients must have had histologic verification of non-CNS solid tumor malignancy at original diagnosis or relapse * Part 2: Patients must have had histologic verification of CNS malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) * Patients must have either measurable or evaluable disease * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50% for patients =\< 16 years of age; Note: neurologic deficits in patients with CNS tumors (Part 2 of the study) must have been relatively stable for at least 7 days prior to study enrollment; 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 fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * Myelosuppressive chemotherapy: at least 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea) * Hematopoietic growth factors: at least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Biologic (anti-neoplastic agent): at least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Immunotherapy: at least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * Monoclonal antibodies: at least 3 half-lives of the antibody after the last dose of a monoclonal antibody * Radiation therapy (XRT): at least 14 days after local palliative XRT (small port); at least 150 days must have elapsed if prior total-body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial bone marrow (BM) radiation * Stem cell infusion without TBI: no evidence of active graft vs host disease and at least 56 days must have elapsed after transplant or stem cell infusion * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment * Patients with known bone marrow metastatic disease will be eligible for study provided they meet the required blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions) * 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: * 0.6 mg/dL (1 to \< 2 years of age) * 0.8 mg/dL (2 to \< 6 years of age) * 1.0 mg/dL (6 to \< 10 years of age) * 1.2 mg/dL (10 to \< 13 years of age) * 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age) * 1.7 mg/dL (male) or 1.4 mg/dL (female) (\>= 16 years of age) * Urine protein: =\< 30 mg/dL in urinalysis or =\< 1+ on dipstick, unless quantitative protein is \< 1,000 mg in a 24-hour urine sample * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Shortening fraction of \>= 27% by echocardiogram OR ejection fraction of \>= 50% by gated radionuclide study * No known cardiac disease * No history of myocardial infarction, severe or unstable angina, peripheral vascular disease or familial corrected QT (QTc) prolongation * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * Nervous system disorders (Common Terminology Criteria for Adverse Events version 4 \[CTCAE v 4\]) resulting from prior therapy must be =\< grade 2 * For Part 2 only: No evidence of new CNS hemorrhage defined as more than punctate size and/or more than three foci of punctate hemorrhage on baseline magnetic resonance imaging (MRI) obtained within 14 days prior to study enrollment * No evidence of active bleeding * Prothrombin time (PT) and partial thromboplastin time (PTT) =\< 1.2 x upper limit of normal (ULN) and an international normalized ratio (INR) =\< 1.2 * A blood pressure (BP) =\< the 95th percentile for age, height, and gender, and not receiving medication for treatment of hypertension * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method for the duration of study participation, and for 6 months after completion of AMG 386 administration * Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anticancer agents are not eligible * Patients who are receiving cyclosporine, tacrolimus, or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients who are currently receiving therapeutic anticoagulation with heparin, low-molecular weight heparin, or Coumadin are not eligible for this trial * Patients who are currently receiving aspirin, ibuprofen, or other non-steroidal anti-inflammatory drugs or anti-platelet agents are not eligible * Patients who are receiving anti-hypertensive medications for control of blood pressure at the time of enrollment are not eligible for this trial * Patients who have an uncontrolled infection are not eligible * Patients who have received a prior solid organ transplantation are not eligible * Patients who have had or are planning to have the following invasive procedures are not eligible: * Major surgical procedure, laparoscopic procedure, open biopsy, or significant traumatic injury within 28 days prior to enrollment * Central line placement or subcutaneous port placement is not considered major surgery but must be placed at least 3 days prior to enrollment for external lines (e.g., Hickman or Broviac) and at least 7 days prior to enrollment for subcutaneous port * Core biopsy within 7 days prior to enrollment * Fine-needle aspirate within 7 days prior to enrollment * Patients with evidence of active bleeding: intratumoral hemorrhage by current imaging, or bleeding diathesis are not eligible * Patients with a history (within 365 days prior to study enrollment) of arterial/venous thromboembolic events including transient ischemic attack (TIA) or cerebrovascular accident (CVA) are not eligible * Patients with a history of hemoptysis within 42 days prior to study enrollment are not eligible * For Part 2: Patients with CNS tumors and evidence of new CNS hemorrhage of more than punctate size and/or more than three foci of punctate hemorrhage on baseline MRI obtained within 14 days prior to study enrollment are not eligible; Note: echocardiogram (ECHO) gradient MRI sequences per institutional guidelines are required for patients with CNS tumors * Patients who have a history of serious or non-healing wound, abdominal fistula, gastrointestinal ulcer or perforation, bone fracture, or intra-abdominal abscess within 28 days of study enrollment are not eligible * Patients with known cardiac or peripheral vascular disease are not eligible * Patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study are not eligible