Vismodegib in Treating Younger Patients With Recurrent or Refractory Medulloblastoma

Inclusion Criteria: * Patients with a histologically confirmed diagnosis of medulloblastoma that is recurrent, progressive, or refractory to standard therapy and for which there is no known curative therapy * Patient must have adequate archival formalin fixed, paraffin embedded (FFPE) primary tumor material for biology studies; specifically, adequate archival FFPE tumor material is either: * An FFPE block, preferably in which tumor occupies an area of at least 10x10 mm if available, and is free of surgical or processing artifacts; tumor in the submitted FFPE block must not have been obtained from the CUSA trap OR * Preferably15x5µm sections if available from an FFPE tissue block conforming to the above criteria AND * Tissue submission must be accompanied by a copy of the pathology report * Patients must have bi-dimensionally measureable disease in the brain or spinal cord defined as at least one lesion that can be accurately measured in at least 2 planes in order to be eligible for this study * Patients must have a body surface area (BSA) of \>= 0.67m\^2 and at most 2.5m\^2 * Patients with neurological deficits should have deficits that are stable for a minimum of 1 week prior to registration; this is to be documented in the database * Karnofsky performance status of \>= 50% in patients \> 16 years, or Lansky performance status of \>= 50% in patients \>= 3 yrs and =\< 16 years, assessed within two weeks prior to registration * Must have recovered from prior treatment-related toxicity; no other myelosuppressive chemotherapy or immunotherapy within 4 weeks prior to study entry (6 weeks if prior nitrosurea) * Decadron dose should also be stable or decreasing for at least 1 week (7days) prior to starting therapy * Radiation therapy (XRT) \>= 3 months prior to study entry for craniospinal irradiation; \>= 8 weeks for local irradiation to primary tumor; \>= 2 weeks prior to study entry for focal irradiation for symptomatic metastatic sites * Off all colony stimulating factors \> 1 week prior to study entry (granulocyte colony stimulating factor \[GCSF\], granulocyte macrophage colony stimulating factor \[GM CSF\], erythropoietin) * Prior therapy will include primary therapy (including radiation therapy and chemotherapy) and a maximum of 2 additional salvage therapies; patients can enroll on the protocol after failure on primary therapy * Absolute neutrophil count (ANC) \>= 1000 µL * Platelet count \>= 50,000/uL (transfusion independent) * Hemoglobin \>= 8.0 gm/dL (may receive red blood cell \[RBC\] transfusions) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70ml/min/1.73 m\^2 or a serum creatinine =\< 1.5 mg/dL * Serum Total Bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamic-pyruvic transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 times institutional ULN for age * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 times institutional ULN for age * Alkaline Phosphatase =\< 1.5 times institutional ULN * Serum albumin \>= 2.5 g/dL * Patient must have recovered from the significant acute toxicities of all prior therapy before entering this study and meet all other eligibility criteria specified in the Inclusion and Exclusion Criteria * Pregnancy should be avoided for 12 months after the last dose of GDC-0449 for females of child-bearing potential; female patients of childbearing potential must not be pregnant or breast-feeding; female patients of childbearing potential must have a negative serum or urine pregnancy test within 24 hours prior to beginning treatment * Women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 10-14 days and within 24 hours prior to the first dose of GDC-0449 (serum or urine); a pregnancy test (serum or urine) will be administered every 4 weeks if their menstrual cycles are regular or every 2 weeks if their cycles are irregular while on study within the 24-hour period prior to the administration of GDC-0449; prior to dispensing GDC-0449, the investigator must confirm and document the patient's use of two contraceptive methods, dates of negative pregnancy test, and confirm the patient's understanding of the of GDC-0449 to cause spontaneous abortion or birth defects; female patients are required to use two forms of acceptable contraception, including one barrier method during participation in the study and for the 12 months following the last dose; all patients should receive contraceptive counseling either by the investigator, or by an obstetrician (OB), gynecologist or other physician who is qualified in this area of expertise; if a woman of childbearing potential believes that her contraceptive method has failed, emergency contraception should be considered; if a patient is suspected to be pregnant, GDC-0449 should be immediately discontinued; in addition, a positive urine test must be confirmed by a serum pregnancy test; if it is confirmed that the patients is not pregnant, the patient may resume dosing with GDC-0449; if a female patient becomes pregnant during therapy or within 12 months after the last dose of GDC-0449, or if the female partner of a male patient exposed to the drug becomes pregnant while the male patient is receiving GDC-0449 or within 12 months after the last dose of GDC-0449, the investigator must be notified in order to facilitate outcome follow-up; female patients should not breastfeed a baby while on this study; female patients must NEVER donate ova while being treated with GDC-0449; all sexually active male subjects (including those who have undergone vasectomy) should utilize a barrier form of contraception during study treatment and for 12 months after the last dose as it is not known whether GDC-0449 that may be present in seminal fluid would cause serious or life-threatening birth defects in a fetus born to the female partner of a male subject; males should also not donate sperm during treatment or up to 12 months after the last dose * Signed informed consent must be obtained including for pharmacokinetic study according to institutional guidelines Exclusion Criteria: * Central nervous system (CNS) embryonal tumor other than medulloblastoma; for example, patients with diagnosis of Atypical Teratoid / Rhabdoid Tumor (ATRT), primitive neuroectodermal tumor (PNET) from a non-cerebellar site within the central nervous system, ependymoblastoma, or medulloepithelioma * Patients with any clinically significant unrelated systemic illness (serious infections or significant cardiac, pulmonary, hepatic or other organ dysfunction), that would compromise the patient's ability to tolerate protocol therapy or would likely interfere with the study procedures or results * Patients receiving any other anticancer or investigational drug therapy, or warfarin * Patients with inability to return for follow-up visits or obtain follow-up studies required to assess toxicity to therapy * Other: below given criteria are confirmed by the patient history * Inability to swallow capsules * Malabsorption syndrome or other condition that would interfere with enteral absorption * History of congestive heart failure * History of ventricular arrhythmia requiring medication * Uncontrolled hypocalcemia, hypomagnesemia, hyponatremia or hypokalemia defined as less than the lower limit of normal for the institution despite adequate electrolyte supplementation * Clinically important history of liver disease, including viral or other hepatitis or cirrhosis