Any cough that lasts longer than a week or 2 really needs a doctor's attention. The smell may indicate an infection. If it doesn't get sorted it could lead to a weakness or susceptibility in future.
The person may have a case of tuberculosis. Have it checked out ASAP. The other reason could be mouth or stomach ulcers. Get this person to a dentist, get their mouth clened, get a tongue scraper and ask them to floss or chew gum when the smell is most noxious.