Cabozantinib-S-Malate in Treating Younger Patients With Recurrent, Refractory, or Newly Diagnosed Sarcomas, Wilms Tumor, or Other Rare Tumors

Upper age limit of =\< 18 years of age for medullary thyroid carcinoma (MTC), renal cell carcinoma (RCC) and hepatocellular carcinoma (HCC) =\< 30 years for all other diagnoses

Patients must have a body surface area \>= 0.35 m\^2

Patients must have recurrent or refractory disease, or newly diagnosed disease with no known curative therapy or therapy proven to prolong survival with an acceptable quality of life; patients must have had histologic verification of one of the malignancies listed below at original diagnosis or at relapse:

* Ewing sarcoma

* Rhabdomyosarcoma (RMS)

* Non-rhabdomyosarcoma soft tissue sarcomas (STS) including microphthalmia transcription factor associated STS (alveolar soft part sarcoma \[ASPS\] and clear cell sarcoma \[CCS\])

* Osteosarcoma

* Wilms tumor

* Rare tumors

* Medullary thyroid carcinoma (MTC)

* Renal cell carcinoma (RCC)

* Hepatocellular carcinoma (HCC)

* Hepatoblastoma

* Adrenal coertex carcinoma

* Pediatric solid tumors (including central nervous system \[CNS\] tumors) with known molecular alterations in the targets of XL184 (i.e., MET amplification, overexpression, activating mutation, MET translocation, MET exon skipping mutations, activating RET mutations, RET rearrangement, overexpression or activation of AXL); documentation of the alteration from a Clinical Laboratory Improvement Act (CLIA) certified laboratory will be required

* Note: Documentation of any known tumor molecular alterations and RET mutation status for patients with MTC (germline) must be uploaded via the RAVE system

Patients must have radiographically measurable disease; measurable disease is defined as the presence of at least one lesion on magnetic resonance imaging (MRI) or computed tomography (CT) scan that can be accurately measured with the longest diameter a minimum of 10 mm in at least one dimension (CT scan slice thickness no greater than 5 mm)

* Note: The following do NOT qualify as measurable disease:

* Malignant fluid collections (e.g., ascites, pleural effusions)

* Bone marrow infiltration

* Lesions only detected by nuclear medicine studies (e.g., bone, gallium or positron emission tomography \[PET\] scans)

* Elevated tumor markers in plasma or cerebrospinal fluid (CSF)

* Previously radiated lesions that have not demonstrated clear progression post radiation

* Leptomeningeal lesions that do not meet the measurement parameters noted above

Patients must have a Lansky or Karnofsky performance status score of \>= 50, corresponding to Eastern Cooperative Oncology Group (ECOG) categories 0, 1 or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score

Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study

Patients with solid tumors must not have received myelosuppressive chemotherapy within 3 weeks of enrollment onto this study (6 weeks if prior nitrosourea)

At least 7 days must have elapsed since the completion of therapy with a growth factor. At least 14 days must have elapsed after receiving pegfilgrastim

Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>= 7 days after the last dose of agent

Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1

\>= 2 weeks must have elapsed since local palliative radiation therapy (XRT) (small port); \>= 6 weeks must have elapsed since treatment with therapeutic doses of M-Iodobenzylguanidine (MIBG); \>= 3 months must have elapsed if prior craniospinal XRT was received, if \>= 50% of the pelvis was irradiated, or if total-body irradiation (TBI) was received; \>= 6 weeks must have elapsed if other substantial bone marrow irradiation was given

* Subjects should not have any clinically relevant ongoing complications from prior radiation therapy (i.e., radiation esophagitis or other inflammation of the viscera)

No evidence of active graft versus (vs.) host disease and \>= 2 months must have elapsed since transplant

Not previously received XL184 or another MET/HGF inhibitor (tivantinib or crizotinib); there are no limits on number of prior therapeutic regimens; patients who have been treated with prior VEGF pathway, or RET inhibitors (except XL184) may be eligible

Peripheral absolute neutrophil count (ANC) \>= 1000/uL for patients with solid tumors without bone marrow involvement

Platelet count \>= 100,000/uL (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) for patients with solid tumors without bone marrow involvement

Hemoglobin \>= 8.0 g/dL (may receive red blood cell \[RBC\] transfusions) for patients with solid tumors without bone marrow involvement

Peripheral absolute neutrophil count (ANC) \>= 750/uL for patients with solid tumors and known bone marrow metastatic disease

Platelet count \>= 50,000/uL for patients with solid tumors and known bone marrow metastatic disease

Hemoglobin \>= 8.0 g/dL for patients with solid tumors and known bone marrow metastatic disease

Transfusions are permitted to meet both the platelet and hemoglobin criteria for patients with known bone marrow metastatic disease; patients must not be known to be refractory to red blood cell or platelet transfusions

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:

* 2 to \< 6 years of age

* Male and female: 0.8 (maximum serum creatinine \[mg/dL\])

* 6 to \< 10 years of age

* Male and female: 1 (maximum serum creatinine \[mg/dL\])

* 10 to \< 13 years of age

* Male and female: 1.2 (maximum serum creatinine \[mg/dL\])

* 13 to \< 16 years of age

* Male 1.5 (maximum serum creatinine \[mg/dL\])

* Female: 1.4 (maximum serum creatinine \[mg/dL\])

* \>= 16 years of age

* Male: 1.7 (maximum serum creatinine \[mg/dL\])

* Female: 1.4 (maximum serum creatinine \[mg/dL\])

Urine protein: =\< 30 mg/dl in urinalysis or =\< 1+ on dipstick, unless quantitative protein is \< 1000 mg in a 24 hour (h) urine sample

Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age

Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 135 U/L (3 x ULN) (for the purpose of this study, the ULN for SGPT is 45 U/L)

Serum albumin \>= 2.8 g/dL

No history of congenital prolonged corrected QT (QTc) syndrome, New York Heart Association (NYHA) class III or IV congestive heart failure (CHF)

No clinically significant cardiac arrhythmias, stroke or myocardial infarction within 6 months prior to enrollment

QTc =\< 480 msec; Note: Patients with grade 1 prolonged QTc (450- 480 msec) at the time of study enrollment should have correctable causes of prolonged QTc addressed if possible (i.e., electrolytes, medications)

Patients with a known seizure disorder who are receiving non-enzyme inducing anticonvulsants and have well-controlled seizures may be enrolled

CNS toxicity =\< grade 2 with the exception of decreased tendon reflex (DTR); any grade of DTR is eligible

International normalized ratio (INR) =\< 1.5

Serum amylase =\< 1.5 x ULN

Serum lipase =\< 1.5 x ULN

What this study is about