The complete sentence Look! is grammatical: an adverb (look where?) can be supplied by an outstretched hand, a nod of the head, a slight movement of the eye, specifying the intended direction. Language "very often" occurs in communicative contexts, between interlocutors, with each utterance having a function. The isolated utterance, lying, as it were, on a laboratory table, is not language.
It may depend on what you define a complete sentence to be. But for one thing, actual communication does not necessarily take place in "complete sentences".
You will have to add a bunch of "elided" components to transform
into a complete sentence.
The man is looking.
can be a meaningful utterance, said
by one interlocutor to another in an actual communicative context in which each utterance has an intended function, and even if such function is not clear it can be sussed out by the hearer perceiving the speaker's intention.
Five people are watching for meteors from about 10pm to 4am on 11-12 August. The people vary in gender and age, one only of them is an adult male (or "man"), and each one of them has an assigned quadrant and schedule. One person will not be actively observing, or looking, at any given 20-minute interval. Who's looking for meteors from 0220 to 0240 in quadrant B? Is it the child Sammy who's looking? No. The man is looking.