James wrote to Christians who had been 'dispersed' due to the railings of Saul of Tarsus. These he wrote to were Christian believers and James's use of dead fsaith means non-functioning faith, not erased or gone out of existence faith. A 'dead faith' is a faith that exists but is non-functioning. James goes on in Chapter four of his letter to explain how to activate such non-functioning faith. He never addresses non-existent faith because he is writing to fellow Christian Jews.
Be careful what you call 'nonsense', especially with your so muddled understanding of the way a Jew in the time of James would use the term you are seeing, dead faith'. It does not mean gone from existence, it refers to non-functioning faith so James writes to explain how to active their faith in Christ.
Fixed it! Ping