Does prayer become void for a paralyzed patient who cannot control what comes out of him, uses diapers, and is unable to purify himself?

If your brother is of sound mind, then prayer is not waived for him, and he must pray according to his ability, even if on his side or back. As for impurities that exit involuntarily, he is not obligated to wash them from his body or clothes due to the difficulty of avoiding them. This is based on the principle of pardon for impurities that are difficult to guard against, such as a persistent, chronic ritual impurity that is continuous with a person.