MySQL LEFT JOIN 3 tables

You are trying to join Person_Fear.PersonID onto Person_Fear.FearID - This doesn't really make sense. You probably want something like:

SELECT Persons.Name, Persons.SS, Fears.Fear FROM Persons
LEFT JOIN Person_Fear
    INNER JOIN Fears
    ON Person_Fear.FearID = Fears.FearID
ON Person_Fear.PersonID = Persons.PersonID

This joins Persons onto Fears via the intermediate table Person_Fear. Because the join between Persons and Person_Fear is a LEFT JOIN, you will get all Persons records.

Alternatively:

SELECT Persons.Name, Persons.SS, Fears.Fear FROM Persons
LEFT JOIN Person_Fear ON Person_Fear.PersonID = Persons.PersonID
LEFT JOIN Fears ON Person_Fear.FearID = Fears.FearID

try this

    SELECT p.Name, p.SS, f.Fear 
    FROM Persons p 
    LEFT JOIN Person_Fear fp 
    ON p.PersonID = fp.PersonID
    LEFT JOIN Fear f
    ON f.FearID = fp.FearID

Try this definitely work.

SELECT p.PersonID AS person_id,
   p.Name, p.SS, 
   f.FearID AS fear_id,
   f.Fear 
   FROM person_fear AS pf 
      LEFT JOIN persons AS p ON pf.PersonID = p.PersonID 
      LEFT JOIN fears AS f ON pf.PersonID = f.FearID 
   WHERE f.FearID = pf.FearID AND p.PersonID = pf.PersonID