When you search a name on Facebook, and that person's name appears on their friends' posts (and you click on the name of the person you are searching for on those posts), it takes you to their (former) page with no information on it other than their profile picture. Does that mean that they only allow friends to search them and see their postings or does that mean that the account is deactivated?
If the name is clickable, it means the profile is active. And when you click on someone's name it will show only those parts of the profile which are public. The profile pic would be visible but if the audience is not set "public" you will not be able to click on that.
You can search for anyone on Facebook but you will only be able to see their public posts if you are not friends with them.