You can't. The phone needs to be able to turn on to get the data off of it. You can try checking the SIM that was in it (if it had one) to see if it 'may' have saved the contacts on it, but in most cases it wouldn't have unless done intentionally. Or if he had a google account that he sent the contacts to (some older flip phones can do that), then he could get them that way.
Your only other option would be to check the account for that phone (online or on paper) which should list all calls in and out with numbers, dates, times, etc., and sort through that to find who is who. It won't have names though.