Palbociclib in Treating Patients With Relapsed or Refractory Rb Positive Advanced Solid Tumors, Non-Hodgkin Lymphoma, or Histiocytic Disorders With Activating Alterations in Cell Cycle Genes (A Pediatric MATCH Treatment Trial)

Inclusion Criteria: * Patient must have enrolled onto APEC1621SC and must have been given a treatment assignment to MATCH to APEC1621I based on the presence of an actionable mutation as defined in APEC1621SC * In addition to the actionable mutations, positive Rb expression by immunohistochemistry is required for study enrollment * Patients must be \>= than 12 months and =\< 21 years of age at the time of study enrollment * Patients must have a body surface area \>= 0.87 m\^2 at enrollment * Patients must have radiographically measurable disease at the time of study enrollment; patients with neuroblastoma who do not have measurable disease but have MIBG+ evaluable disease are eligible; measurable disease in patients with CNS involvement is defined as any lesion that is at minimum 10 mm in one dimension on standard magnetic resonance imaging (MRI) or computed tomography (CT). * Note: The following do not qualify as measurable disease: * Malignant fluid collections (e.g., ascites, pleural effusions) * Bone marrow infiltration except that detected by MIBG scan for neuroblastoma * Lesions only detected by nuclear medicine studies (e.g., bone, gallium or positron emission tomography \[PET\] scans) except as noted for neuroblastoma * Elevated tumor markers in plasma or cerebrospinal fluid (CSF) * Previously radiated lesions that have not demonstrated clear progression post radiation * Leptomeningeal lesions that do not meet the measurement requirement…