About a year ago, I had to hire someone for a part-time (29 hour) job on my team. I started getting emails from someone who had, a few years earlier, been a Sr. VP in another division. Now, apart from the fact that she had no experience in the specific skills I was looking for, there was no way I was going to hire someone who once far outranked me in the company. And the HR people didn't even put her on the short list of people to be interviewed. I ended up hiring someone who was coming off an internship with another unit in my division and for whom this job was the next logical step in her career.
Good choice, that would be worse than the usual overqualified candidate, somebody used to being in charge in that company would just be a nightmare.