This expression must be a hyperbole, an exaggeration. Most of the time when we fall, no one is there is pick us up, let alone falling straight into someone's arms. The act of falling into someone's arms would mean that you didn't experience the hard fall that was expected. They saved you some pain like a scrapped knee. In literature, it usually refers to when a woman falls in love with a man. He "catches" her in a sense. He finds her interesting enough a person to begin a relationship with her. The woman is saved the hard fall of not having a man who cares for her. Of course, it is proper to have the scene reversed when a guy falls into a girl's arms. Equal rights, you know.