Is "Which made him run out the door in fear." A sentence or fragment (incomplete sentence).

This is fragment; it doesn't tell us why he ran out of the door in fear.

It's a fragment because complex sentences (ones that contain subordinating conjunctions) usually contain 2 parts: a independent sentence, and a dependent fragment. In your example, the phrase only contains a dependent clause and doesn't give the full information like that of a sentence, therefore, it is a fragment.