Two quick points: First, nearly 100% of the people I contact will tell me they are very happy where they are and have no interest in making a change. I usually will explain to them that's one of the reasons I'm calling them. When I'm making contact on someone's behalf it's not as though they want me calling unhappy and disgruntled people so that they can go somewhere and make the people there miserable also.
Secondly, I don't think there are too many recruiters that want to have a role in people moving to a 'sinking' ship. An exception would be if someone is being courted for their 'turn around' skills and the situation is presented that way up front.
My situation is a little unique in that I don't recruit people for open positions. If I locate a candidate that meets certain criteria, the companies I recruit for will gladly make a place for them.