Vincristine Sulfate, Topotecan Hydrochloride, and Cyclophosphamide With or Without Bevacizumab in Treating Young Patients With Refractory or First Recurrent Extracranial Ewing Sarcoma

Inclusion Criteria: * ALT =\< 5 times ULN for age * Urine protein: creatinine ratio =\< 0.5 OR 24-hour urine protein \< 1,000 mg * At least 6 weeks since other prior substantial bone marrow radiation * At least 28 days since prior major surgical procedures (e.g., resection of tumor, laparotomy, thoracotomy, or open biopsy) * At least 2 weeks since prior myelosuppressive chemotherapy (4 weeks for nitrosoureas) * At least 2 weeks since prior local palliative radiotherapy (e.g., small port) * Diagnosis of extracranial Ewing sarcoma or primitive neuroectodermal tumor of bone or soft tissue meeting 1 of the following criteria: I) a first recurrence of localized disease; II) a first recurrence of initially metastatic disease; III) disease refractory to initial conventional therapy * Patients must have RECIST-measurable disease documented by clinical, radiographic, or histological criteria * Patients who do not have measurable disease (e.g., bone scan-determined metastatic disease only) remain eligible for the study and will be evaluable for disease-free progression * Karnofsky performance status (PS) 50-100% (\> 16 years of age) OR Lansky PS 50-100% (=\< 16 years of age ) * Life expectancy \>= 8 weeks * Absolute neutrophil count \>= 1,000/μL * NOTE: Patients with tumor metastatic to bone marrow are permitted to receive transfusions to maintain hemoglobin and platelet counts. These patients will not be evaluable for hematologic toxicity. Patients who are refractory to platelet infusions (i.e., unable to maintain platelet counts \> 75,000/μL) and have marrow involvement and platelet counts \< 75,000/μL are not eligible * Fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy * At least 1 week since prior therapy with a biologic agent or growth factor * Patients must have histological verification of the malignancy at original diagnosis * Histological confirmation of relapse is highly recommended but not mandatory * Prior initial therapy with topotecan hydrochloride is allowed as long as \> 2 years have elapsed since the initial diagnosis of Ewing sarcoma * Prior therapy with cyclophosphamide or vincristine is allowed * Minor surgical procedures (e.g., biopsies) for limited purposes of tissue retrieval allowed * Minor procedures include indwelling IV catheter placement and needle biopsy for diagnostic purposes * For minor surgeries, patients should not receive the first planned dose of bevacizumab until the wound is healed and 7 days have elapsed * At least 6 months since prior craniospinal radiotherapy or radiotherapy to \>= 50% of the pelvis * At least 3 months since prior autologous stem cell transplantation (SCT) * Platelet count \>= 75,000/μL (transfusion independent) * Hemoglobin \>= 8.0 g/dL (may receive RBC transfusions) * Direct bilirubin =\< 1.5 times upper limit of normal (ULN) for age * Creatinine clearance or radioisotope GFR \>= 70 mL/min OR serum creatinine normal for age * Hypertension must be well controlled on stable doses of medication for \>= 2 weeks prior to enrollment * Negative pregnancy test * Female patients who are lactating must agree to stop breast-feeding * II) The patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * Shortening fraction \> 28% OR ejection fraction \> 50% * Recovered from any prior surgical procedure * Sexually active patients of childbearing potential must agree to use effective contraception * Patients on full-dose anticoagulants (e.g., warfarin) with PT INR \> 1.5 are eligible if both of these criteria are met: * I) The patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin Exclusion Criteria: * Radiological or clinical evidence for parenchymal brain metastases or neuro axis involvement * Documented, chronic nonhealing wound, ulcer, or significant traumatic injury (those with bone fractures, including pathological fractures, or requiring surgical intervention) within the past 28 days * Other bone complications * Deep venous thrombosis (including pulmonary embolism) within the past 3 months * Recent (i.e., within 6 months) arterial thromboembolic events, including transient ischemic attack or cerebrovascular accident * History of myocardial infarction, severe or unstable angina, or peripheral vascular disease Prior bevacizumab * Radiotherapy or surgery for local control of recurrent disease concurrently with bevacizumab (bevacizumab must be held if radiotherapy or surgery is required) * Radiotherapy to localized painful lesions is allowed, provided \>= 1 measurable lesion is not irradiated * Radiotherapy for local metastatic tumor control allowed after the first 2 courses of therapy * Other cancer chemotherapy or immunomodulating agents * Steroid use is allowed * Prior allogeneic SCT