Update: Facebook started to show the announced prompt and ask for user consent.
Almost a year after it removed the option for 90% of its members, Facebook informed on Wednesday the remaining 10% that they’ll remove the “Who can search my timeline by name” setting in a few days. Removing this setting si likely a violation of the 2011 FTC settlement.
Timeline concealed to the public
A month ago Facebook announced that they’ll prompt user to get their consent before removing the setting 
but they finally decided to just inform users with an email and a very short notice displayed above the News Feed.
In the mail sent to its members, Facebook argues that when they created this setting “the only way to find [them] on Facebook was to search for [their ]specific name. Now, people can come across [their] Timeline in other ways: for example if a friend tags [them] in a photo, which links to [their]Timeline, or if people search for phrases like “People who like The Beatles,” or “People who live in Seattle,” in Graph Search”. However, I’m confident that some users – including me — are not tagged in public photo, do not like public content and have no friend whose “friends list” is public.
Timelines of these users will not appear in public Graph Search results Facebook and there is no public link that could be used to find them. As a matter of fact, people who are not my friends (or friends of friends) can’t even know if I have a Facebook account. As for today, the only solution to find my Facebook Timeline is to test the 1.2 billion userID numbers. In addition to be time consuming, this exhaustive search would violate Facebook Terms of Services.
Private vs Nonpublic
A Timeline page is public because any user can load its content but Timelines URLs (i.e. usernames) are not public since not anyone can find them: without the search functionality, it is not possible to retrieve the Timeline associated to a specific user. Timelines URLs are like unlisted phone numbers or Google Docs shared with “anyone with the link”. These documents may not be seen as private but I would not define them as public (i.e. I’d be unpleasantly surprised to see them used in an endorsed advertisement). I do not claim that Timelines are private, only that they are “nonpublic user information” .
Why Facebook could violate the FTC settlement
The FTC settlement does not focus on user private information but cover the entire nonpublic user information (e.g. a user ID to which access is restricted by a privacy setting). Indeed, Section II-A of the 2011 settlement requires that Facebook “prior to any sharing of a user’s nonpublic user information by [Facebook] with any third party, which materially exceeds the restrictions imposed by a user’s privacy setting (s), shall […] obtain the user’s affirmative express consent”.
Facebook will not only remove the possibility to select who can look-up timelines, they will set the setting to its default values “Everyone”. Hence, Facebook will modify settings of users who set it to a more restricted audience. Obviously the two lines message Facebook displayed and the email they sent to the affected members does not offer a valid solution to get an affirmative express consent. So Facebook will certainly violate the FTC settlement in a few days.