In the case of darker works, this light may be ephemeral. But the chance must be there for the girl to escape the knife-wielding psycho. Even if there is no way out, the audience must think there is. Only then, can the true fear take root.
Once the slaughter becomes monotonous, the most desperate victim will throw up their hands and submit to the axe. It is the persistence of hope gnawing away at the reader, which will ensure the terror is maintained until the final cut. The true moment of fright is not when the killer has someone in his clutches, but just before the grasping hand snatches its prize.
With other types of stories, hope also plays an invaluable role. In drama, a tragedy will typically engender sympathies and a desire for the suffering to have some sort of end. Readers can be sadistic though, and often demand a great deal of pain before their emotional limit is reached.
The more you like the characters, the stronger your yearnings will be for their eventual happiness. Hope approaches unawares, and readers weep for those they have come to hold dear. At that point, a nudge in any direction will have a profound effect on the emotions.
Stories are a journey into the unknown. A satisfying ending is not always a happy one. But there must be hope: lurking in a corner somewhere, perhaps just out of reach as the trembling victim hides behind a flimsy door.