Ask HN: Reverse Recruiting

Hi everyone. Going anon for obvious reasons. I'm a C-Level exec who just got semi-mutually moved from my position. It wasn't a good fit, but sucks nonetheless.

Anyway, I get a decent amount of inbound recruiting from LinkedIn, but I was curious if there is any (or if it's advisable) to go the other direction -- to work with an agency and let them know that I'm available. I know the pyramid narrows quite a bit at the C-Level.