I would imagine that you could hire a private investigator.
Most employers today won't do much more than verify dates of employment. Many employers are even afraid to tell an investigator whether the person was fired, quit, etc. They are afraid of being sued. A good background investigator will usually find out one way or another. Often times the investigator will locate and speak with friends or previous co-workers, etc. to find out information that employers might be reluctant to divulge about the subject (record or no record). Often times co-workers provide a more accurate picture of what kind of employee the subject was.