Whenever a member of a team has been terminated, there will be impacts on the psyches of the other members of the team. A manager must work carefully to make sure that the motivation of the other team members will not be compromised.
One thing that a manager might do is to say as much as possible, within the limits of privacy policies, to explain why the team member was terminated. Other team members will naturally be worried that they are going to be next. The manager needs to let them know as much as possible about why the other member was let go so that they can have some sort of gauge as to how safe their jobs are. They will want to know, for example, that firing decisions are not made capriciously. They will also want to know if the measure was related to cost-cutting and, if so, if more cuts are likely.
Another thing that a manager should do is to clearly address issues of how the team will work with its new personnel setup. Team members will be concerned about what the loss of a team member will mean in terms of division of labor and responsibility. It is a good idea to spell this out clearly so that team members will know what will be expected of them going forward. This is also vital to morale.
So, overall, there needs to be a lot of communication so as to ensure that morale and motivation do not suffer in the wake of the termination.