Any reputable instructor will carry a policy protecting against personal liability. Further, students are generally required to sign waivers for the instructor and for the range in use, if they are two distinct entities. I know your question is in regards to future events and not just the day of training, but I will get to that.
In order for the instructor to be held liable there would have to be a gross negligence on the part of the instructor. That would entail presenting a technique or providing information that is so blatantly wrong that it would shock a reasonable person.
A simple disagreement in the way that material is presented or delivered is generally not cause for incurring liability, i.e. Weaver vs. Isocoles stances. "Well, if he (instructor) had taught my client to stand square to the target the round would have hit the bullet resistant vest instead of entering under the arm." That is a difference in methodologies and not cause for liability.
However, it is possible that an instructor could incur liability if their teachings are outside of the accepted norms of the firearms community. "It is ok to dry fire your weapon at someone as long as you know the weapon is clear." Such statements that are so shocking are likely not to be covered under even the best of policies. It would probably be determined that no reasonable instructor would give such advice.
Another item that would likely be addressed is whether or not the person is actually an "instructor." A personal peeve of mine, but it seems that just about anyone is willing to call themselves an instructor, regardless of any credentials that would support such a claim. When a person obtains an insurance policy as a firearms instructor they must generally attest by signature that they are indeed an accredited/certified instructor (by NRA, military, police, etc). Many are not yet sign as such. Some "instructors" call themselves such because they think they've gone to enough "you name it" schools as a student to self qualify themselves as an instructor, hold a super duper rating in bowling pin shooting, or are "self taught" and just "good enough to teach." If they are found out, the coverage is likely null and void.
The long and short of it is this. If the person is an accredited instructor, carrying a valid certificate of liability insurance, and presenting techniques/information that is reasonable based upon established and traditional training regimes, it is highly unlikely that they will be held personally liable for an event occurring outside of their immediate dominion and control.