The problem seems to really get sticky when that one person creates conflict, obstructs progress, refuses to leave the past, opposes everything, and is simmering with anger. Not fun. But very safe for them.
First, you can't change this behavior. The more rigidly an individual clings to what she has decided is righteous or the more obsessively she clings to the past, the even-less anyone can do. Understand that people in that space don't want to be positive or see successful solutions; they want to ruminate. And they will employ many different psychological tactics to keep themselves safely planted in the past.
What you can do is attempt to understand it. Practice tolerance. Extend, within yourself, compassion for their misery. Then walk away. If they are part of a group in decision-making, step around them. Why?
Because they cannot see another perspective and they are unwilling to change. There are deep-rooted reasons for that.
Some people don't mature beyond young adolescence. The world is black and white, no shades of gray. Absolutes. And most of us grown-ups know the world is chalk-full of gray. To cope, an adult of less maturity seeks, seizes, and is obsessive in controlling everything. If there are multiple possibilities, the predominant feeling of the individual is fear: OH MY GOD, THIS IS THREATENING! And so, the afflicted person seeks, with all their might, to control and dominate the uncertainty - while more mature individuals are capable of tolerating ambiguity.
Some people can't move forward. They are living in the past, ruminating over every grievance - even ones that don't fit the reality of others. The chains that keep them bound to the past have nothing to do with the actions of other people or situations. The links in the chains that bind them are anger, stubbornness, lack of compassion, jealousy, and blaming of others. It isn't other people that keep this sort of person trapped - it's the entitled role of victim that they enjoy wearing. It's familiar. And within that familiarity is some kind of payoff for them.
Another psychological tactic is displacement. I recently had someone tell me that my information, from two real estate attorneys, a title officer, a real estate broker, and my own research, was not 'reliable'. This came from a person who had been misinforming everyone of three things for eight years. But it's safer to call another individual not reliable than to admit your own lack of reliability with information.
Then there is the oppositional person. I sat at a meeting recently, dominated by an oppositional person. It was really something. For every statement, she had an opposite statement. When it was noted that a tree had been trimmed to reveal the sign, she interrupted to say, We haven't done it for years and the sign is still bent. When the legal counsel explained the uselessness of a very expensive document from 10 years ago, her response was But nothing ever gets done, and it's fiscally irresponsible. There is no exchange here. In a room of seventeen people, every single sentence spoken by another was argued, interrupted, obstructed and defeated. Do not expect a situation like this to ever be productive.
So, walk away. None of the bitterness, ruminating, clinging to past issues, or other pettiness can be reasoned with or negotiated. It's not coming from the situation or the people - it is generated solely within the individual afflicted with issues that prevent cooperative endeavors. You can't fix it, and you'll never change it, because you lie outside of them and they must be the agent of their own change.
So my advice is walk away. In a group, step around. Then go home and have a margarita. I have a hint for you, an already-tequila-infused-preparation. Two words: Sandra Lee.