How would you manage/lead a project team during a reorganisation of the company. The project itself has nothing to do with the reorg, but the people are affected: some change departments, some are presented different working conditions. All decided above their heads. And all the while, when peoples lives are affected, you have to maintain focus on the project vision and deliverables.
This is a very difficult situation to be in, and I speak from experience!
No matter what you, as PM, may say, the team members who are affected will have their own perspective on this. The best that you can hope to do is provide a structured environment where they can immerse themselves in their work. You may be expected to be a sympathetic ear to the concerns of the team: this is fine up to a point, but if you end up being the person that they all pour out their hearts to, but can't do anything about the situation, you will lose respect and authority, so be careful.
When this happened in my place of work, I met with the team and made sure that they understood what I could - and more importantly, what I could not - do to change the situation. I then reminded them of the objectives of the project, and asked them to tell me directly (and individually- not in the open forum) if they saw any specific barriers to success. This allowed them to think about the impact of the re-organisation on their work, rather than on their personal situations.
This worked up to a point, but if people are upset and / or worried, it doesn't matter what you say: they will still be worried until they see how they are actually impacted by the new structure.
I'm not certain you, yourself, can repair the situation other than gently reminding the survivors that there is still work to do and what needs doing. Be professional, and try to remind them to be professional as well. Restructurings, reorganizations and layoffs always introduce significant amounts of fear, uncertainty and doubt. The clearest cure would come from the top, as senior leadership can quickly squash rumors with open, honest facts. When uncertainty outperforms truth from above, then every rumor could be true and workers will treat every rumor as if it were true. When rumors rule, fear triumphs.
I'm currently listening to Predictably Irrational, and chapter 4 goes on about the difference between social norms and market norms. One of the key points the author was making is that folks typically work harder when motivated by social norms (which is why many companies try to introduce such norms by pushing for the "we're all family" approach). When social norms get replaced by market norms, people who had the social norm attitude feel betrayed, and it can take years to recover from that betrayal. If any of your senior leadership is saying "it's nothing personal, it's just business" then they've totally repudiated all social norms in favor of market norms.
I've been there. It's difficult. You need to look at this from two different perspectives. 1- your projects. You are the PM and you need to advise your sponsor on how to manage the impact on your project. Does this mean your project might get delayed? That it should be canceled? If you didn't identify loss of team members as a risk, then deal with it as an issue. 2 - the people. As the PM you are viewed as a leader (or should be) and your job is to support the organizational goals and help people through the change. Do this by honesty and respect, don't minimize the impact, don't over dramatize the impact.
It can be done. When this happened at my company, I led a team of PMs and ran major enterprise wide projects - and my job was eliminated. Over a 2 month period I had to close down the projects - most of the key team members were downsized - and keep my PMs motivated and focused on going forward.