It depends, of course
If it is a character that I know well, I'll usually let the cosplayer run with their ideas and then I would add or propose changes to the idea to get the shot. Once they run out of ideas then I'll propose my own based on what I know of the anime/manga/game and character. If its an original creation or I have no idea about the anime/manga/gam , then I'll talk with the cosplayer for a few minutes to get the story behind their character, why they chose the character, what story do they want to tell, what emotions do they want to portray.
If you are setting this up in advance, let photog know what you want or at least give them some source material such as images you like, AMV or video clips of the anime/game. This has helped me in the past when I had never seen the anime that they want to shoot. I could get the general feel of the anime and even take some screenshots that I could use to help with poses. All in all, I think collaborations work well because the more input the better and have a clear idea of what you want and communicate that to the photographer.
"Destiny is not a matter of chance; it is a matter of choice. It is not a thing to be waited for; it is a thing to be achieved."- William Jennings Bryan (1860 - 1925)