A clause constituent can be an essential element, such as a subject or predicate, an adjunct, such as an object or related phrase, or an element belonging to a possessive or descriptive construction.
This does not license omission of an essential element everywhere. A contextual clue is necessary. In answer to “Who arrived?”, replying “Zayd” may leave the verb unspoken because the question supplies it. Similar contextual recoverability is required for ellipsis in Arabic discourse.
Grammatical labeling alone is not enough; the listener must be able to understand what is omitted.