Cabozantinib S-malate in Treating Patients With Relapsed Osteosarcoma or Ewing Sarcoma

Inclusion Criteria: * Young patient age between 12 - 15 could be included in only 6 centers (Bordeaux, Lyon, Villejuif, Lille, Marseille and Paris) * Patients must have histologically confirmed diagnosis of osteosarcoma or Ewing sarcoma by central review, except if the diagnosis was already confirmed by the RRePS (Reseau de Reference en Pathologie des Sarcomes et des Tissus Mous et des Visceres) network * Relapsed disease after standard chemotherapy * Patients must have measurable disease (lesion in previously irradiated field could be considered as measurable if progressive at inclusion) defined as per RECIST v1.1 with at least one lesion that can be measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm with spiral computed tomography (CT) scan * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Life expectancy of greater than 3 months * Absolute neutrophil count \>= 1,500/mcL * Lymphocyte count \> 1,000/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional upper limit of normal * Creatinine =\< 1.5 x ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (Cockcroft formula) * Hemoglobin \>= 9 g/dL * Serum albumin \>= 2.8 g/dL * Lipase \< 2.0 x ULN …