And yet there is a thriving market for paying people to get your child into their first-choice college...
I Can Get Your Kid into an Ivy
I would suggest that such a service could be done on a contingency basis, and fees are not paid until a job is offered and accepted.
A good headhunter knows all the unadvertised positions and reqs and would have a list of jobseekers ready to be matched up to them. Of course, the headhunter would be able to turn down a client whom he feels he could not help.