Vismodegib in Treating Patients With Recurrent or Refractory Medulloblastoma

Inclusion Criteria:

* Patients with a histologically confirmed diagnosis of medulloblastoma (including posterior fossa PNET) that is recurrent, progressive, or refractory to standard therapy and for which there is no known curative therapy are eligible; there must be evidence of residual measurable disease or lesion in pre-study MRI as described in section; patients with spinal disease that is measurable will be eligible
* The diagnosis should be confirmed at the treating institution and tissue (either from the diagnosis or relapse or preferably from both time points) must be available for biological studies
* 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
* Eastern Cooperative Oncology Group (ECOG) performance status 0- 2
* No other myelosuppressive chemotherapy or immunotherapy within 4 weeks prior to study entry (6 weeks if prior nitrosourea)
* 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 (\>= 23 Gy); \>= 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 (GCSF, GM CSF, erythropoietin)
* Absolute neutrophil count (ANC) \>= 1000/μL
* Platelet count \>= 50,000/uL (transfusion independent)
* Hemoglobin \>= 8.0 gm/dL (may receive RBC transfusions)
* Creatinine clearance or radio-isotope GFR \>= 70ml/min/1.73 m2 or
* A serum creatinine =\< 2.0 mg/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age
* Serum glutamic pyruvic transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x institutional ULN
* Serum glutamic-oxalacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2.5 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
* 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 use 2 forms of acceptable contraception, including one barrier method during participation in the study and for the 12 months following the last dose; for medical or personal reasons, 100% commitment to abstinence is considered an acceptable form of birth control. All patients should receive contraceptive counseling either by the investigator, or by an OB/gynecologist or other physician who is qualified in this area of expertise; 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
* Signed informed consent according to institutional guidelines must be obtained

Exclusion Criteria:

* 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
* Patients with inability to return for follow-up visits or obtain follow-up studies required to assess toxicity to therapy
* Life expectancy \< 12 weeks as determined by treating physician
* Inability to swallow capsules
* Prior treatment with GDC-0449 or other antagonists of the HH pathway
* 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
* Congenital long QT syndrome