The succession was broken at the fifth Chinese patriarch, and has never been restored.
The rank of patriarch could be the more easily discontinued because he had no ruling power. He was simply a defender, teacher, and example of the Buddhist doctrine and life.
The following paragraphs are taken from papers I wrote many years ago.
After the death of Shakyamuni, or, to speak honorifically, his entrance into the Nirvana at Kushinagara, a series of thirty-three patriarchs, if we include five Chinese holders of the dignity, superintended in succession the affairs of the religious community he had founded. Remusat has given an abstract of the biography of the patriarchs taken from a Japanese encyclopaedia. He says, Buddha, before his death, committed the secret of his mysteries to his disciple, Maha Kashiapa. He was a Brahman, born in the
kingdom Magadha, in Central India. To him was intrusted the deposit of esoteric doctrine, called Cheng fa-yen-tsang, "the pure secret of the eye of right doctrine." The symbol of this esoteric principle, communicated orally without books, is man or wan. This, in Chinese, means "10,000," and implies the possession of 10,000 perfections. It is usually placed on the heart of Buddha in images and pictures of that divinity. It is sometimes called sin-yin, "heart's seal." It contains within it the whole mind of Buddha. In Sanscrit it is called svastika. It was the monogram of Vishnu and Shiva, the battle-axe of Thor in Scandinavian inscriptions, an ornament on the crowns of the Bonpa deities in Thibet, and a favourite symbol with the Peruvians.
The appointment of Kashiapa to be successor of Buddha and patriarch is described in the following manner:--"The World-honoured teacher ascended the platform from which he gave his instructions, holding in his hand a flower, the gift of a king. His disciples were all regardless of his teaching. Only Kashiapa showed attention and pleasure in his countenance. Buddha understood what was passing in his mind, and gave him the pure mystery of right doctrine, the secret heart of the Nirvana, that true knowledge of existing things which consists in knowing them not to exist, and the method of enlightenment and reformation."
Kashiapa distinguished himself by severely ascetic practices. Buddha knew his excellence, and wished him to sit on the same seat with himself, as being not inferior in merit. But to this he would not consent. He also easily comprehended the ideas of Buddha. Buddha, on one occasion, used the following illustration:--"A notable man's house took fire. He brought goat-carts, drawn by goats, deer, and bullocks, to rescue his sons. He afterwards gave them a lofty, broad waggon, drawn by white bullocks. The first are the methods of Hinayana. The last is that of Mahayana." Kashiapa understood that