What kind of sentence does not have a subject and verb?

A sentence that does not have a subject and verb is called a fragment.

Here are some examples of fragments:

* Running down the street. (Missing subject)

* Because the weather was nice. (Missing subject and main verb)

* With a smile on her face. (Missing subject and main verb)

Fragments are grammatically incomplete and cannot stand alone as a complete thought. They often function as dependent clauses, needing a main clause to make sense.