Clinical Research Directory

Inclusion Criteria: * Patients must have histologically confirmed diagnosis of chondrosarcoma (conventional, mesenchymal, dedifferentiated or clear cell subtypes) * Patients must have measurable disease (outside any previously irradiated field) defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm with spiral computed tomography (CT) scan * No more than three prior lines of chemotherapy for advanced disease (including no more than 450 mg/m\^2 doxorubicin); at least three weeks since last chemotherapy (six weeks in case of nitrosoureas and mitomycin C), immunotherapy or any other pharmacological treatment and/or radiotherapy * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \> 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Metastatic or unresectable locally advanced disease * Documented disease progression (as per RECIST) before study entry * Women of child-bearing potential and men must use two forms of contraception (i.e., barrier contraception and one other method of contraception) at least 4 weeks prior to study entry, for the duration of study participation, and for at least 24 months post-treatment for female patients and for 2 months for male patients; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 7 days prior to initiation of GDC-0449 (serum or urine); a pregnancy test (serum or urine) will be administered every 4 weeks while on study within the 24-hour period prior to the administration of GDC-0449; a positive urine test must be confirmed by a serum pregnancy test; 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 teratogenic potential of GDC-0449 * Women of childbearing potential are defined as follows: * Patients with regular menses * Patients with amenorrhea, irregular cycles, or using a contraceptive method that precludes withdrawal bleeding * Women who have had a tubal ligation * Women are considered not to be of childbearing potential for the following reasons: * The patient has undergone hysterectomy and/or bilateral oophorectomy * The patient is post-menopausal defined by amenorrhea for at least 1 year in a woman \> 50 years old * The patient has permanent premature ovarian failure confirmed by specialist gynecologist * Ability to understand and the willingness to sign a written informed consent document * In accordance with French Regulatory Authorities: Patients with French Social Security in compliance with the French law relating to biomedical research (Huriet Law 88-1138 and related decrees) Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to GDC-0449 or other agents used in the study * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption; patients must be able to swallow capsules * Patients with clinically important history of liver disease, including viral or other hepatitis, or cirrhosis are ineligible * Patients with uncontrolled hypocalcemia, hypomagnesemia, hyponatremia, or hypokalemia defined as less than the lower limit of normal for the institution, despite adequate electrolyte supplementation, are excluded from this study * Tumor tissue sample not available for pathological review and/or correlative studies * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with GDC-0449; these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible