HR Consulting firms?

I noticed that a few HR consulting firms reach out to people with higher experiences to fulfill an opening that their clients have. I suspect they reach out to anyone with less than 5 or 7 years of experience. Also, I noticed that consultants from these HR firms tend to focus on a certain specific roles/department when hiring.

Have you approached any one such HR consulting firm for a job change? If yes, provide their name and the role you were looking for. What is the fee they charge (if they do)?