Not often. (Hasn't happened to me yet, in 38 years.) But it can happen.
Suits where the instructor is the primary defendant normally revolve around the instructor injuring the student.
Vicarious liability, in which the plaintiff sues everyone in sight, is something I haven't seen happen yet to a CCW instructor after the graduate shot a third party later in self-defense. (Doesn't mean it hasn't happened, or can't happen; just means I haven't personally seen it.) However, I've seen police lawsuits where everyone from the chief on down was sued by the plaintiff under the vicarious liability theory.