I think this post from Trello's blog gets at what you are looking for: http://blog.trello.com/using-multiple-boards-for-a-super-flexible-workflow/
The tools they are talking about will allow you to accomplish what you want. Except, for your purposes you would want to reverse the workflow diagram they are showing here. Instead of all the cards eventually moving onto one board, you want to have your single prospects board, and be moving candidates off it at different stages of the game.
The key will be building the diagram of your process to make it clear and simple to execute.
For example, there may be several reasons why you would want to remove someone from the process, but keep their information around (They weren't available, they were a great fit but didn't have the right experience, they were overqualified, etc.) Each of those could get board.
Then each department/position type could get a list on the board.
Or maybe these get flipped: Departments get their own board, and reasons for removal are the pre-defined lists.
Either way, notes about the position, experience, their recruiter, the exact decision process to remove, etc., can be placed on the card, passed form board to board, and referred to when considering future hiring decisions.