mysql hvordan man finder, om mindst én række fra krydsreferencetabellen er null eller kriterier

Dette lyder som en klassisk usecase for EXISTS operatør:

SELECT *
FROM   mytable a
WHERE  EXISTS (SELECT 1
               FROM   mytable b
               WHERE  a.foreignkey = b.foreignkey 
               AND    trainer IS NOT NULL 
               AND    trainer <> 'FREE'

EDIT:
Hvis du bare vil have den distinkte anderledes foreignkey s:

SELECT DISTINCT foreignkey
FROM   mytable a
WHERE  EXISTS (SELECT 1
               FROM   mytable b
               WHERE  a.foreignkey = b.foreignkey 
               AND    trainer IS NOT NULL 
               AND    trainer <> 'FREE'