Ellipsis occurs at several grammatical levels. An omitted muḍāf can leave its possessor expressed; an omitted qualified noun can leave its adjective; a verb’s complement, object, referent or a whole clause can be understood but unspoken.
An omitted construct noun: “ask the town,” meaning its people.
An omitted qualified noun: a description whose referent is understood.
An omitted verbal complement: the verb’s target is recoverable without repetition.
An omitted conditional response: the consequence can be understood although it is unexpressed.
The analytical task is not merely to label something “omitted,” but to identify what is implied and which linguistic or contextual evidence supports that reading.