Large query with subquery runs indefinitely after mysql update
This does not work in MYSQL?
Give it a try - what do you have to lose?

SELECT people.id, max(results.date) 
FROM people 
JOIN results 
      on people.id = results.person_id 
     and people.boss_id = 123 
GROUP BY people.id;


Would benefit from indexes on:
1) results.person_id
2) people.boss_id   

Index on date may help but start without