Palbociclib Isethionate in Treating Younger Patients With Recurrent, Progressive, or Refractory Central Nervous System Tumors

Inclusion Criteria:

* Patients with retinoblastoma protein (Rb1) positive recurrent, progressive or refractory central nervous system (CNS) tumors
* Histologically confirmed Rb1 positive primary recurrent, progressive, or refractory central nervous system tumors; patients with low grade gliomas are excluded
* Formalin fixed paraffin embedded tumor tissue (preferably from current recurrence) must be available to assess Rb1 protein status prior to enrollment; only patients with recurrent diffuse intrinsic brain stem glioma (DIPG) can be enrolled without the need for available tumor tissue for Rb1 protein status confirmation
* Patients must have measurable disease (in 2-dimensions) on magnetic resonance imaging (MRI) scan of brain and/or spine to assess preliminary evidence of response
* Body surface area (BSA):

  * Patients enrolled on dose level 1 (50 mg/m\^2) must have BSA \>= 1.20 m\^2
  * Patients enrolled on dose level 2 (75 mg/m\^2) must have BSA \>= 0.93 m\^2
  * Patients enrolled on dose level 3 (95 mg/m\^2) must have BSA \>= 0.70 m\^2
* Patients must have received no more than 2 prior chemotherapy regimens and/or focal radiotherapy for their brain tumor and fully recovered from the acute treatment related toxicities of all prior therapies prior to entering this study; for those acute baseline adverse events attributable to prior therapy, patients must meet organ function criteria
* Chemotherapy: patients must have received their last dose of known myelosuppressive anticancer chemotherapy at least three (3) weeks prior to study enrollment in the study or at least six (6) weeks for those receiving nitrosourea
* Biologic therapy: patients should have received their last dose of biologic agent \>= 7 days prior to enrollment; in the event the patient has received another biologic agent and has experienced \>= grade 2 myelosuppression, then at least three (3) weeks must have elapsed prior to enrollment; if the investigational or biologic agent has a prolonged half-life then at least three (3) weeks interval is required
* Radiotherapy: patients must have had their last fraction of:

  \* Focal irradiation \> 2 weeks prior to enrollment
* Corticosteroids: patients who are receiving dexamethasone or other corticosteroids must be on a stable or decreasing dose for at least 1 week prior to enrollment; it is recommended that patients be off all steroid therapy or receive the least dose that will control their neurologic symptoms
* Growth factors: all colony forming growth factor(s) have been discontinued for at least one week prior to enrollment (filgrastim, sargramostim, and erythropoietin); for patients on long acting growth factors, the interval should be two weeks
* Patients with neurological deficits that are stable for a minimum of one week prior to registration
* Patients must be able to swallow capsules
* Karnofsky performance scale (KPS for \> 16 years of age) or Lansky performance score (LPS for =\< 16 years of age) assessed within two weeks of enrollment must be \>= 60
* Absolute neutrophil count \>= 1,000/mm\^3
* Platelets \>= 100,000/mm\^3 transfusion independent (no platelet transfusion one week prior to enrollment)
* Hemoglobin \>= 8 g/dl
* Total bilirubin =\< 1.5 times upper limit of institutional normal (ULN) for age
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal for age
* Serum albumin \>= 3 g/dL
* 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 (male), 0.6 (female)
  * 2 to \< 6 years: 0.8 (male), 0.8 (female)
  * 6 to \< 10 years: 1 (male), 1 (female)
  * 10 to \< 13 years: 1.2 (male), 1.2 (female)
  * 13 to \< 16 years: 1.5 (male), 1.4 (female)
  * \>= 16 years: 1.7 (male), 1.4 (female)
* Female patients of childbearing potential must have a negative serum pregnancy test at the time of enrollment
* Patients of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control while being treated on this study
* Patient and/or guardian have the ability to understand and the willingness to sign a written informed consent document according to institutional guidelines

Exclusion Criteria:

* Patients with any clinical significant unrelated systemic illness (serious infections or significant cardiac, pulmonary, hepatic or other organ dysfunction) that is likely to interfere with the study procedures or results
* Patients with low grade gliomas and Rb1 negative tumors
* Patients who have received any of the following:

  * \> 2 chemotherapy regimens
  * Myeloablative chemotherapy with stem cell rescue
  * Craniospinal irradiation
* Patients with corrected QT (QTc) interval of \> 450 msec or those on medications known to prolong QTc interval
* Prior treatment on a CDK inhibitor
* Patients who are receiving drugs that are strong inducers or inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4)
* Patients who are receiving any other investigational therapy
* Patients who require enzyme inducing anti-convulsants to control seizures
* Patients with cataracts on ophthalmologic examination