Probably the most typical reason for foul breath in cats is dental disease. The bacteria in plaque and tartar buildup give forth an unpleasant smell. The accumulation can result in gingivitis, which then fuels gum disease and ultimately tooth loss.
If left untreated, oral wounds, growths, and ulcers can produce an unpleasant odor. These can get worse by oral bacteria. Stomatitis or another issue could be the reason behind these lesions. These not only smell horribly unpleasant, but cats typically find them to be very uncomfortable. Additionally, severe kidney illness or uncontrolled diabetes can cause bad breath.