CAMPFIRE: A Study of Abemaciclib (LY2835219) in Participants With Ewing's Sarcoma

Inclusion Criteria: * Diagnosis of Ewing's sarcoma or Ewing's sarcoma-like tumor by institutional pathologist. The original pathological report is required. Repeat biopsy at progression is not required * Refractory disease or confirmed radiological progression or recurrence following first or later line of treatment of Ewing's sarcoma or Ewing's sarcoma-like tumor \-- Must have one measurable or evaluable lesion per RECIST 1.1 * Adequate performance status based on age * For participants less than (\<)16 years of age, a Lansky score greater than or equal to (≥)50, or * For participants ≥16 years of age, a Karnofsky score ≥50 * Participants must have discontinued all previous treatments for cancer or investigational agents ≥7 days after the last dose and must have recovered from the acute effects * Adequate hematologic and organ function less than or equal to (≤)14 days prior to Day 1 of Cycle 1: * Absolute neutrophil count ≥1000/microliter (µL) * Platelets ≥75,000/cubic millimeter (mm³) * Hemoglobin ≥8 grams per deciLiter (g/Dl) (≥100 grams per Liter \[g/L\]) * Total bilirubin ≤1.5 times (×) upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤3 × ULN * Creatinine clearance or calculated glomerular filtration rate (GFR) ≥60 milliliters per minute per square meter (Ml/min/m²) or serum creatinine based on age/gender * Female participants of childbearing potential must have a negative urine or serum pregnancy te…