There are many good answers in Is there a way to say "go to the path of no way out"?, but most of them imply that the subject is aware of the situation after making the mistake (like "Oh shit! I've painted myself into the corner."). I want to find a phrase or idiom to emphasize the unawareness of getting lost, that they are going down the path leading nowhere. They don't know what they don't know, and without outside help they will keep going, thinking that someday the solution will come. In Buddhism term, they haven't reached nirvana and is still stuck in the samsara.
So far, I only see that "going down the path leading nowhere" is the most suitable. But I'd like to see other options.