Ellipsis works only when the listener can recover the subject from an indication. The cue may come from an earlier sentence, the current exchange, a gesture, or a situation that fixes the referent. The subject's absence from the wording does not mean it must be absent from the listener's understanding.
UtteranceInterpretation
Q: «كَيْفَ زَيْدٌ؟» A: «مَرِيضٌ»The question identifies the subject; omission is intelligible.
«مَرِيضٌ» without contextThe listener may not know who is ill.
The presence of an indication is a condition for intelligibility; the specific rhetorical advantage is a separate issue. First establish that the omission can be resolved; then explain why leaving the subject unsaid improves the utterance.