At death's door means very seriously ill or near death. The correct answer is this meaning because the expression is used figuratively, not only by its literal words.

Examples:

• After the accident, the patient seemed at death's door.
• In an HSC essay, At death's door can express this meaning: very seriously ill or near death.
• When this expression appears in a passage, connect At death's door with the idea of very seriously ill or near death.