There's a short story where a young artist tries to get recognition for her work. She goes to every gallery, meets every critic, but all doors are closed to her. In the end, she gives up and the story ends. There's no hope of a future breakthrough shown, just the dead end of her artistic dreams. This is an example of a 'dead end short story'.
Sure. Consider a short story where a man is searching for a lost love in a big city. He follows every lead, but in the end, he realizes that she has moved on and he'll never find her again. The story just ends there, at the point of his realization. That's a dead end short story.