Headed in example sentence
The Finzi-Contini's, however, believe that their position of wealth and their very home will shield them from being touched, and they move on, oblivious to the world outside, in a frozen period of time and space that seems, for a moment, to spare them, until it becomes rather clear that the walls that so protected them are beginning to crumble and that they are headed towards an inevitable train wreck which will destroy all that they know.