 They knew he needed it. As bad as the debate was for Mr. Biden, the worst moment of the night came later after Mr. Biden had been gingerly guided down the steps and shuffled off the stage and onto another one for a post-debate vigil. Bathed in fake applause, Mr. Biden looked particularly cadaverous and weary with the strings of his thin white hair matted down close to his scalp. He looked confused. He looked vacant. His mouth was open.