Prexasertib in Treating Pediatric Patients With Recurrent or Refractory Solid Tumors

Inclusion Criteria:

* Patients with recurrent or refractory solid tumors, including central nervous system (CNS) tumors, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or in 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 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 therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment; if after the required timeframe, the defined eligibility criteria are met, e.g. blood count criteria, the patient is considered to have recovered adequately

  * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive; the duration of this interval must be discussed with the study chair and the study-assigned research coordinator prior to enrollment

    * \>= 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea)
  * Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>= 7 days must have elapsed from last dose of agent; the duration of this interval must be discussed with the study chair and the study-assigned research coordinator prior to enrollment
  * Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1
  * Corticosteroids: If used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid
  * Hematopoietic growth factors: \>= 14 days must have elapsed since the last dose of a long-acting growth factor (e.g. pegfilgrastim) 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 and the study-assigned research coordinator
  * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days must have elapsed since the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors)
  * Stem cell infusions (with or without total body irradiation \[TBI\]):

    * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: \>= 84 days must have elapsed after infusion, and no evidence of graft-versus-host disease (GVHD)
    * Autologous stem cell infusion including boost infusion: \>= 42 days must have elapsed after completion
  * Cellular therapy: \>= 42 days must have elapsed since the completion of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.)
  * X ray (XRT)/external beam irradiation including protons: \>= 14 days must have elapsed after local XRT; \>= 150 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial bone marrow (BM) radiation
  * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131 iodine metaiodobenzylguanidine \[131I-MIBG\]): \>= 42 days must have elapsed since systemically administered radiopharmaceutical therapy
  * Patients must not have received prior exposure to LY2606368
* For patients with solid tumors without known bone marrow involvement:

  * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3
  * Platelet count \>= 75,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
  * Hemoglobin \>= 8.0 g/dl at baseline (may receive packed red blood cell \[PRBC\] transfusions)
* Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least 5 of every cohort of 6 patients must be evaluable for hematologic toxicity for the dose-escalation part of the study; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70ml/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:

  * Age: maximum serum creatinine (mg/dL)
  * 1 to \< 2 years: 0.6 (male and female)
  * 2 to \< 6 years: 0.8 (male and female)
  * 6 to \< 10 years: 1 (male and female)
  * 10 to \< 13 years: 1.2 (male and female)
  * 13 to \< 16 years: 1.5 (male), 1.4 (female)
  * \>= 16 years: 1.7 (male), 1.4 (female)
* Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 135 U/L (3x ULN); 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
* Corrected QT (QTc) =\< 480 msec

  * Note: Patients should avoid concomitant medication known or suspected to prolong QTc interval or cause Torsades De Pointes; If possible, alternative agents should be considered
  * Patients who are receiving drugs that prolong the QTc are eligible if the drug is necessary and no alternatives are available
* Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled
* Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\]4) resulting from prior therapy must be =\< grade 2
* For patients with CNS tumors, any baseline neurologic deficit, including seizures, must be stable for at least one week prior to initiating study treatment
* 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
* Tissue blocks or slides must be sent if available; if tissue blocks or slides are unavailable, the study chair must be notified prior to study enrollment

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 both during and for 3 months after participation in this study; abstinence is an acceptable method of contraception
* Corticosteroids: Patients receiving corticosteroids must have been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment; if used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid
* Investigational drugs: Patients who are currently receiving another investigational drug are not eligible
* Anti-cancer agents: Patients who are currently receiving other anti-cancer agents are not eligible
* Anti-GVHD agents post-transplant: 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
* Strong CYP1A2 inhibitors: Patients must not have received strong CYP1A2 inhibitors (ciprofloxacin, fluvoxamine, zafirlukast) for at least 7 days prior to enrollment and must not receive them for the duration of the study
* Patients who have an uncontrolled infection are not eligible
* Patients who have received a prior solid organ transplantation are not eligible
* Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to LY2606368 or to its formulation 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