The purpose of this study is to find out what effects, good and/or bad, a drug called vemurafenib, either alone or combined with another treatment called radioactive iodine, has on the patient and thyroid cancer. It is not known if vemurafenib works against thyroid cancer. This study will test in a small number of patients if it can be used with radioactive iodine to treat thyroid cancers. This type of study is called a pilot study. If the results are positive, a larger study with more patients may be done to further test this treatment.