This was not a dormant faith, it was an active, living, obedient faith that was demonstrated by works. All these, through faith, acted . It was their faith in God that motivated them to perform righteous works. It was their faith that defined them, guided them, and ultimately saved them. For consider Him who has endured such hostility by sinners against Himself, so that you may not grow weary and lose heart.
Faith involves being faithful.
That doesn't mean he is still alive because of what he believes. It means that he lives according to what his faith demands, and that is obedience and loyalty. Of course that faith must be based on hearing and understanding the Word of God, for blind faith will make you fall in the pit. There are those who say that salvation is by faith apart from any works or acts of obedience, and even without baptism. Paul answers that idea in Romans 6, where he tells us that it is in baptism that we get into Christ, are buried into his death, and are raised up to newness of life.