INSERT INTO with subquery that might return 0 results
INSERT INTO status (status1, subject_id) 
SELECT 'processing', u.subject_id 
    FROM users AS u
    LEFT OUTER JOIN status ON (u.subject_id = status.subject_id)
    WHERE (status.status1 IS NULL or status.status1 = 'ready')
      and usrs.start_date IS NOT NULL LIMIT 1
ON CONFLICT (subject_id) DO update SET status1 = 'processing'

PS. LIMIT without ORDER BY is a lottery...