Sorafenib Tosylate in Treating Younger Patients With Relapsed or Refractory Rhabdomyosarcoma, Wilms Tumor, Liver Cancer, or Thyroid Cancer

Patients must have had histologic verification of one of the malignancies listed below at original diagnosis or at relapse:

* Rhabdomyosarcoma (RMS)

* Wilms tumor

* Hepatocellular carcinoma (HCC)

* Papillary thyroid carcinoma (PTC)

Patients must have relapsed or refractory disease (RMS, Wilms tumor, HCC, PTC)

* 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)

* 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 requirements noted above

Patients with HCC must be relapsed or refractory to conventional chemotherapy

Patients with PTC must be refractory to radioactive iodine (RAI)

Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life

Patients with known metastasis to the brain will be excluded from trial participation unless treated surgically or with radiotherapy and stable with no recurrent lesions for at least 3 months

Rhabdomyosarcoma and Wilms strata: patients must be ≥ 24 months and ≤ 30 years of age at study enrollment

Hepatocellular carcinoma (HCC): patients must be ≥ 24 months and \< 18 years of age at study enrollment

Papillary thyroid carcinoma (PTC): patients must be ≥ 24 months and ≤ 21 years of age at study enrollment

Patients must have a Lansky or Karnofsky performance status score of ≥ 50%, corresponding to 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

Peripheral absolute neutrophil count (ANC) ≥ 1,000/μL

Platelet count ≥ 75,000/μL (transfusion independent, defined as not receiving platelet transfusions within a 7-day period prior to enrollment)

Hemoglobin 8.0 g/dL (may receive red blood cell\[RBC\] transfusions)

Creatinine clearance or radioisotope glomerular filtration rate(GFR) 70 mL/min OR a serum creatinine based on age/gender as follows:

* 0.8 mg/dL (2 to \< 6 years of age)

* 1.0 mg/dL (6 to \< 10 years of age)

* 1.2 mg/dL (10 to \< 13 years of age)

* 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age)

* 1.7 mg/dL (male) or 1.4 mg/dL (female) (≥ 16 years of age)

Total bilirubin ≤ 1.5 times upper limit of normal (ULN) for age

SGPT (ALT) ≤ 135 U/L (for the purpose of this study, the ULN for SGPT is 45 U/L)

PT, PTT, and INR \< 1.5 times ULN

Normal serum lipase and amylase (per institutional normal values)

No evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94% if there is clinical indication for determination

A blood pressure (BP) ≤ the 95\^th percentile for age, height, and gender; and not receiving medication for treatment of hypertension

What this study is about