The 1st generation Moto X had a special minimal chip used just to detect you saying "Ok Google Now" (or a custom phrase) to turn the phone on when it was sleepi

The 1st generation Moto X had a special minimal chip used just to detect you saying "Ok Google Now" (or a custom phrase) to turn the phone on when it was sleeping. But I think phones that only detect a start word when the screen is on probably don't have custom low-power hardware for it.