How to see if a person has facebook account deactived or permanent deleted?

You can deactivate your account temporarily and choose to come back whenever you want.

To deactivate your account:

1. Click the account menu
at the top right of any Facebook page
2. Select Settings
3. Click Security in the left column
4. Choose Deactivate your account then follow the steps to confirm

If you deactivate your account your profile won’t be visible to other people on Facebook and people won’t be able to search for you, though some information, such as messages you sent to friends, may still be visible to others.

I don't believe that information is generally available to the public, as it could endanger people who leave FB due to stalking.

However, that being said, you can search for that person's name within FB or on Google (name plus the word Facebook). Check if there's a difference when signed into Google or not, or if you clear cookies or if you use Bing or Yahoo! to search.

Do not expect this to be a definitive answer to your question because, like I said, there are legitimate privacy and safety concerns against this data being readily available.

If they deactivate their account and they were on your friends list you can still search your friends and find them, but you can’t click on their name to view anything because the account is no-longer active.

If they deleted their account you won’t find them at all, same goes if they blocked you.