Final answer:
A Cricothyrotomy is indicated for a patient who cannot be ventilated by other means and whose oxygen saturation is rapidly declining; it is a lifesaving surgical procedure to establish an airway.
Step-by-step explanation:
For a patient who cannot be ventilated by mask or by Laryngeal Mask Airway (LMA), or intubated, and whose oxygen saturation is falling quickly, the indicated emergency procedure is a Cricothyrotomy. This is a surgical procedure where an incision is made in the cricothyroid membrane to establish an airway for ventilation. It is considered a lifesaving technique when other methods of securing an airway have failed, and is quicker and easier to perform in emergency situations compared to other techniques such as Retrograde wire intubation, Blind nasal intubation, or Fiberoptic intubation, which may not be feasible or timely under urgent conditions.