Hi Zhenni,
You raised an interesting question. In my opinion Close Project and Phase process group is a process where you close out your project when your customer accepted and sign-off the final deliverable, document lessons learned, and provide a final report summarizing the project performance. I cannot think of any EEF that would have influence the closing process. One example I can think of now is project termination due to company bankruptcy, however, terminating a project due to company bankruptcy would have been an exit criteria written in the project charter (which is already an input to this process group). Besides, to close out this terminated project, it would involved mainly documenting lessons learned and provide a final report on why the project is closed, I don't see any EEF as an input in this process.
I hope someone with more experience will be able to provide a better answer

.