Here is a glaring example of a sentence fragment: Because of the rain. On its own, because of the rain doesn't form a complete thought. It leaves us wondering what happened because of the rain.
Some sentence fragments start with subordinates. Some examples of subordinators are 'when', 'after', 'although', 'before', 'if', 'since', 'until', 'when', 'where', 'while', and 'why'. Sentence fragments can also be phrases.