I understand that an accident or incident by a newly certificated pilot can lead to an enforcement action against his/her instructor.
Only if the investigation uncovers some improper conduct by the instructor during the course of the pilot's training, like signing the pilot off without giving all the required training. That would be violation of several Part 61 sections, including 61.59.
How long is the instructor "on the hook" for this sort of thing.
Theoretically, forever, since the 6-month clock doesn't start running until the FAA becomes aware of the violation by the instructor.
How often does it happen?
Pretty rare, and usually if it happens while the trainee is still a Student Pilot.
For the record, I ask because I'm interested in getting an instructor rating.
Don't worry about it. Play by the book, get good CFI insurance (like the NAFI-sponsored policy from Falcon), document training properly, and don't sign endorsements unless you really believe the trainee meets the standards, and you shouldn't have a problem. For more on this, see "
Does This Tiger have a Tail," written by an aviation attorney for an aviation law conference.
The more likely issue is that if the trainee shows deficiencies in skill or knowledge, the instructor might be called in so the FAA can confirm that the instructor is competent to teach. This could involve a reexamination or "709 ride" on the instructor's CFI ticket covering the areas of concern. It's rare for that to occur on a single event, but if several of your trainees have problems (accidents, incidents, violations, and/or practical test failures), it's something the FAA may do.