Some organs can invaginate.    From Wordnet, Princeton University. 

Such a gastrula, formed mainly by overgrowth of the epiblast, is called an epibolic gastrula, as distinguished from the invaginate gastrula of amphioxus.    From Wordnik.com.  [Text Book of Biology, Part 1: Vertebrata] Reference

—These consist of two highly vascular inflexions of the tela chorioidea, which invaginate the lower part of the roof of the ventricle and are everywhere covered by the epithelial lining of the cavity.    From Wordnik.com.  [IX. Neurology. 4a. The Hind-brain or Rhombencephalon] Reference

It is covered by and adherent to a fold of pia mater, named the tela chorioidea of the third ventricle, from the under surface of which a pair of vascular fringed processes, the choroid plexuses of the third ventricle, project downward, one on either side of the middle line, and invaginate the epithelial roof into the ventricular cavity.    From Wordnik.com.  [IX. Neurology. 4c. The Fore-brain or Prosencephalon] Reference