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 test * Body weight ≥10 kilograms (kg) * Must be able to swallow and/or have a gastric/nasogastric tube \-- Participants in the European Union must be able to swallow intact capsules * Stable or decreasing dose of steroids at least 7 days prior to enrollment * Life expectancy of at least 8 weeks and able to complete at least 1 cycle of treatment * Participants/caregivers are able and willing to make themselves available for the duration of the study and are willing to follow study procedures, including adherence to the pharmacokinetic (PK) sampling schedule Exclusion Criteria: * Participants with severe and/or uncontrolled concurrent medical disease or psychiatric illness/social situation that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol * Participants with an active fungal, bacterial, and/or known severe viral infection including, but not limited to, human immunodeficiency virus (HIV) or viral (A, B, or C) hepatitis. * Participants who have had allogeneic bone marrow or solid organ transplant * Surgery: Participants who have had, or are planning to have, the following invasive procedures: * Major surgical procedure, laparoscopic procedure, or significant traumatic injury within 28 days prior to enrollment * Surgical or other wounds must be adequately healed prior to enrollment * Female participants who are pregnant or breastfeeding * Have received any prior cyclin-dependent kinase (CDK) 4 and 6 inhibitor * Progression during prior treatment with irinotecan and/or temozolomide * Have a known intolerability or hypersensitivity to any of the study treatments or dacarbazine * Diagnosed and/or treated additional malignancy within 3 years prior to enrollment