Denosumab in Treating Patients With Recurrent or Refractory Osteosarcoma

Inclusion Criteria: * Female patients must have a bone age of equal to or greater than 12 years of age as determined by local read of appropriate radiographic imaging * Male patients must have a bone age of equal to or greater than 14 years of age as determined by local read of appropriate radiographic imaging * Patients must have relapsed or become refractory to conventional therapy, with a regimen including some combination of high dose methotrexate, doxorubicin, cisplatin, ifosfamide and etoposide; and have had histologic verification of osteosarcoma at original diagnosis or at the time of recurrence * Cohort 1 patients must have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Cohort 2 patients must have had a complete resection of all sites of metastatic disease within 30 days prior to enrollment * Patients will only be eligible after they have undergone complete surgical resection of suspected metastatic disease that is histopathologically confirmed to be osteosarcoma prior to enrollment * Note: the definition of complete resections is: gross resection of all disease as per the operating surgeon; post-operative imaging is not required for confirmation of complete resection * Patients must undergo resection of any lung lesion meeting criteria for likely metastatic disease, defined as: * 3 or more lesions \> 5 mm in diameter OR a single lesion \> 1 cm * Patients with lung as the only site of resected metastatic disease must have refused participation in protocol AOST1421 * Note: This applies if AOST1421 is open to enrollment at the enrolling institution on the day the patient consents * Patient must have adequate tumor specimen available for submission * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age: 11 to \< 13 years old; 1.2 (male, female) maximum serum creatinine (mg/dL) * Age: 13 to \< 16 years old; 1.5 (male), 1.4 (female) maximum serum creatinine (mg/dL) * Age: \>= 16 years old; 1.7 (male), 1.4 (female) maximum serum creatinine (mg/dL) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 2.5 x ULN for age * Serum calcium or albumin-adjusted serum calcium \>= 2.0 mmol/L (8.0 mg/dL) and =\< 2.9 mmol/L (11.5 mg/dL) Exclusion Criteria: * Patients with known sensitivity to any of the products to be administered during the study (eg, mammalian derived products, calcium or vitamin D) * Patients who are receiving other cancer directed therapy at the time of enrollment * Patients who have previously received denosumab * Patients who have previously received mithramycin, strontium-89, samarium-153 or rhenium * Patients receiving bisphosphonates * Pre-existing conditions * Disorders associated with abnormal bone metabolism * Hypocalcemia that is not corrected with oral calcium supplementation * Vitamin D \< 20 mg/mL * Paget's disease * Prior history or current evidence of osteonecrosis of the jaw * Any dental or oral condition likely to result in disruption of mucosal integrity during denosumab therapy including: active dental or jaw condition requiring oral surgery or tooth extraction; non-healed dental or oral surgery or planned invasive dental procedures during the anticipated course of study therapy * Unstable systemic disease, excluding osteosarcoma, such as unstable proximal renal tubule dysfunction (Fanconi syndrome) or congestive heart failure * Pregnancy and breast feeding * Female patients who are pregnant; a pregnancy test is required for female patients of childbearing potential * Lactating females who plan to breastfeed their infants while on study therapy and through 5 months after completion of study therapy * Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation and for 5 months after the end of study treatment * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met