Going at it with a skilled bummed out player is exhausting but is not particularly difficult. Be careful bummed out is a regular pattern of play for the specific player. Watch that it is not an indication of depression in a colleague who is normally not that way. The key is to see that the authentic bummed out player goes into the routine mostly when he receives criticism or when there are problems. If you are looking for it, the pattern is easy to spot.
Consider first what the dynamics of the play are. The bummed out player is using the technique to avoid responsibility, to get others to back off, and to avoid work or pressure. In a child, the pattern would be called pouting.
Once you spot the bummed out player and understand his behavior, the next step is to locate his protector. No, it will do no good to confront the protector. He either will not hear you or will in some other way refuse to do anything about the problem.
When the player plays or the protector protects, it is time for counter Play. It also will do little good to talk with the bummed out player about his behavior, but it cannot hurt. At least talking about the problem helps put the player on notice that he will not be successful playing the game with you. Whether you talk to the player or not, there are two actions that are necessary and almost always effective over time.
First, simply out wait him. Bring up a problem or issue of concern and then wait for a response other than the bummed out kinds of things discussed above. If necessary, say, "I hear all that. My concern is . . . I'm waiting for your response to the problem." Patiently go back again and again until an appropriate response comes. If necessary, say, "I can see you are not going to deal with this, and I do not have time to play your game. Have your response to me in writing in two hours."
The idea is first to respond only to positive and productive behavior. Next, set things up so such behavior is expected and required. At first, the player will likely not follow through or do what you expect. When this happens, it is time to say, "I expected you would handle this. It seems to me you are either unwilling or unable to deal with these kinds of things. Since it is important, I'm going to take some other action to be sure it gets done. It's too bad you are unable to handle your job. We will need to talk about that soon." Do what needs to be done to get the job done. Interestingly, the bummed out player is likely to do the job himself the next time.
You will be well-advised to think about where these confrontations take place. The bummed out player has a tendency to sit and not talk or respond. If this happens in your office, it may be difficult to stop the process, to get the player out of your office, and get onto other things. If the interaction or lack of interaction is somewhere else, you can be the one to leave. This makes it more convenient and keeps the player from having control of your space.
Sooner or later - and probably sooner - you will need to deal with the player's protector. He will come to the aid and defense of the player. Especially, if the protector is your organizational equal or superior, it is not a good idea to confront him about his protector role.
If the protector confronts you about your approach with the player, say, "I am not sure what you are talking about. Andy (the player) seems to be having a rough time of it. My problem is getting the job done. All I did was to make arrangements to be sure the job gets done. Andy needs to work out his problems, but we need to take care of business in the meantime. If Andy can do the job, that will be terrific. If not, the job still has to be done. Why don't you talk to him about that? Maybe you can help him work out whatever the problem is. You seem to have a special relationship with him. I just need to be sure the work gets done, one way or the other." Even the most committed protector is likely to understand and accept this kind of reasoning. If not, he is likely another experienced player who needs to be managed separately from the original player.