By "frozen" do you mean that you don't want for work items to be added to/removed from/edited within the completed iteration? If that's what's changing the KPIs that you referred to then unfortunately there's no permission-based way to do what you're describing. You can buffer against this to some extent by ensuring that you change the State of the iteration to Accepted in Plan >> Timeboxes >> Iterations, which will remove the iteration from most dropdowns in work item detail pages.
I can see the business logic in your request but there doesn't appear to be anything like it currently in Agile Central Idea Manager, so you might want to add an idea there and promote it here in the forums. Hope that helps.