Anyone know of a Dystopian-like Anime in an underground setting with a young seemingly weak protagonist who turns out to be very powerful?

I first watched this series (one or two episodes) in the Anime Club at the college I attended. It likely has a Dystopian underground sort of setting (something similar to City of Ember). All I recall is one episode where the protagonist (a boy with white hair) is trudging through a labyrinth or tunnel, perhaps to pass some sort of trial, despite being injured and about to lose the will to carry on yet pushes forward.

So far I have not been able to find this anime, any help and/or title suggestions would be appreciated. Thanks!