Which of the following is an example of an improperly used subordinate clause? a. rainsford swam to the island. after he fell off the boat. b. even though the sniper was in pain, he continued to shoot. c. the sniper was focused, despite his hunger, exhaustion, and pain. d. the sniper, with his ever-changing feelings, is revealed as a dramatic character.

A subordinate clause is a clause that follows a conjunction and is dependent on the main clause. Another name for a subordinate clause is a dependent clause.  The subordinate clause begins with a subordinate conjunction or a relative pronoun. It also contains a subject and a verb. It is important to note that the subordinate clause does not form a complete sentence. It's aim and purpose is to encourage the reader to want additional information to finish the thought. 

The following clauses are example of an improperly used subordinate clause:
A. Rainsford swam to the island. 
C. The sniper was focused, despite his hunger, exhaustion, and pain.
D. The sniper, with his ever-changing feelings, is revealed as a dramatic character.

The correct answer is A - that is the one sentence which has the improper use of subordinate clause, whereas all the other sentences are correct. (Because 'sniper' refers to the man, not to the gun. If it referred to the gun, all of them would be incorrect). However, C and D don't have subordinate clauses.
Still, if I had to choose one, I'd go with A - because the sentence is written incorrectly, they have to be merged into one sentence - After he fell off the boat, Rainsford swam to the island.