Entinostat in Treating Pediatric Patients With Recurrent or Refractory Solid Tumors

Inclusion Criteria:

* Patients must have a body surface area (BSA) of \>= 1.17 m\^2 at time of study enrollment
* Patients must be able to swallow intact tablets
* Patients with recurrent or refractory solid tumors, including central nervous system (CNS) tumors or lymphoma, 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 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

    * Solid tumor patients: \>= 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea)
    * Lymphoma patients:

      * a waiting period prior to enrollment is not required for patients receiving standard cytotoxic maintenance chemotherapy (i.e. corticosteroid, vincristine, thioguanine\[6MP\], and/or methotrexate)
      * \>=14 days must have elapsed after the completion of other cytotoxic therapy, with the exception of hydroxyurea, for patients not receiving standard maintenance therapy; additionally, patients must have fully recovered from all acute toxic effects of prior therapy; Note: cytoreduction with hydroxyurea must be discontinued \>= 24 hours prior to the start of protocol therapy
  * 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 the 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
  * Hematopoietic growth factors: \>= 14 days must have elapsed from 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 from the last dose of interleukins, interferon or cytokines (other than hematopoietic growth factors)
  * Stem cell infusions (with or without traumatic brain injury \[TBI\]):

    * 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 from infusion and no evidence of graft versus host disease (GVHD)
    * Autologous stem cell infusion including boost infusion: \>= 42 days must have elapsed from infusion
  * Cellular therapy: \>= 42 days must have elapsed from last dose of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.)
  * External beam radiation (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, iobenguane I-131 \[131I-MIBG\]): \>= 42 days must have elapsed from the last dose of systemically administered radiopharmaceutical therapy
  * Histone deacetylase (HDAC) inhibitors: Patients must not have received prior therapy with entinostat; patients who have received therapy with other HDAC inhibitors are eligible
* Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 (within 7 days prior to enrollment)
* Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) (within 7 days prior to enrollment)
* Hemoglobin \>= 8.0 g/dl, with or without transfusion (within 7 days prior to enrollment)
* Patients with known bone marrow metastatic disease will not be eligible
* 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:

  * 1 to \< 2 years: 0.6 mg/dL for males and females
  * 2 to \< 6 years: 0.8 mg/dL for males and females
  * 6 to \< 10 years: 1.0 mg/dL for males and females
  * 10 to \< 13 years: 1.2 mg/dL for males and females
  * 13 to \< 16 years: 1.5 mg/dL for males and 1.4 mg/dL for females
  * \> = 16 years: 1.7 mg/dL for males and 1.4 mg/dL for females (within 7 days prior to enrollment)
* Bilirubin (sum of conjugated + conjugated) =\< 1.5 x upper limit of normal (ULN) for age (within 7 days prior to enrollment)
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3 x upper limit of normal (ULN) = 135 U/l; for the purpose of this study, the ULN for SGPT is 45 U/l (within 7 days prior to enrollment)
* Serum albumin \>= 2 g/dl (within 7 days prior to enrollment)
* 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 both during and for 3 months after participation in this study; abstinence is an acceptable method of contraception; those who become pregnant while on treatment with entinostat must discontinue immediately and consult their treating physician
* 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; if used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid
* Patients who are currently receiving another investigational drug are not eligible
* Patients who are currently receiving other anti-cancer agents are not eligible
* Patients requiring concurrent administration of valproic acid are not eligible for this trial
* 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 with a BSA ˂ 1.17 m\^2 at time of study enrollment are not eligible
* Patients who are not able to swallow intact tablets are not eligible
* Patients with a known history of corrected QT (QTc) prolongation (\> 480 msec), or known history of ventricular tachycardia, ventricular fibrillation or Torsades de pointes are not eligible
* Patients who have an uncontrolled infection are not eligible
* Patients who have received a prior solid organ transplantation 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
* Patients with a history of allergy to medications that have a benzamide structure (e.g., metoclopramide, procarbazine, domperidone, cisapride etc.) are not eligible