A second type of fragment is the subordinate clause that is incorrectly separated from the sentence in which it belongs. A clause is a group of words containing a subject and predicate and used as a part of a sentence. A subordinate clause does not express a complete thought and cannot stand alone.
Chapter 11 Sentence Completeness, Fragments and Run-on Sentences, in Warriner's English Grammar and Composition Revised Edition, Complete Course, John E. Warriner and Francis Griffith, 1965