[Reyna Evergreen]

Because we know that the Ring had somekind of way of getting around, I guess that the wearer would stay invisible until the Ring found some way of rubbing againts someting, or slipping off (ect...) and then the corpse would be revealed, much to the dismay of the finder.

This is all just an assumption, though. Maybe, in retrospect, the Ring just stayed, invisible, with the Bearer until he or she was reduced to nothing...

But because Tolkien never intended a Bearer to die, all we can do is guess...