Recently, this process came to an end, and now FB no longer supports searching users information based on their global ID/username, that includes their Profile pictures.
For example, while Mark Zuckerberg has an active Facebook account:
His Facebook account's details (including the profile picture) are unavailable publicly as they used to be:
If you're utilizing your own FB app, you should use the unique, app-dedicated, user ID which was provided to you by Facebook (for every user who signs to it) in order to fetch this user's profile image.
Cloudinary will continue supporting only those app-dedicated user IDs as Facebook deprecated the support of global ID searching (URL conventions haven't been changed).