It’s a simple question and it probably justifies an equally simple answer. I can think of two possible reasons; the first of which is probably the correct one. Your cat is using the litter box and it is not uncommon, as you might imagine, for domestic cats to walk on their poop when they are in the litter box. They can then track the poop on their paws into the home with some litter substrate. An annoying thing to happen.
So, your cat will be clean except perhaps for some poop in between his or her toes. But that scenario would not last that long in my view because domestic cats are very good at cleaning their toes. However, it might last long enough for an owner to believe that their cat smells of poop even when they look clean.
Under the circumstances it might also pay to check the quality of a cat’s poop. There might be diarrhoea and then you will need to assess the cause of diarrhoea which is a symptom of illness, but it may simply be the food that the cat has eaten.
The advantage of litter boxes is that you can check poop and therefore conduct an analysis of your cat’s health to a certain extent working backwards from the quality of their faeces (the linked page covers this extensively but concisely).
Flatulence
Another possibility is that your cat is passing a lot of wind. Like people, cats can have gassy bowels and pass wind more than normal. Domestic cats who pass wind a lot can be an embarrassment if there are visitors to the home! It’s also distressing.
Flatulence (a better term for this condition) is caused by eating highly fermentable foods. These might be beans, cauliflower or cabbage (what kind of cat eats cabbage!). Or they might be drinking large quantities of milk (more likely) and finally they might be swallowing large amounts of air when eating.
This is a dietary problem and diets high in carbohydrates and fibre can contribute to flatulence. And malabsorption of the food in the intestine can also lead to flatulence. This is about incomplete digestion of carbohydrates. Try specially prepared cat milk of no milk at all.
The fix is to firstly rule out malabsorption syndrome. You will need a vet’s advice on that. You can change a cat’s diet to a highly digestible, low-fibre one. A switch from commercial food to a highly digestible prescription diet might work.
Hill’s do Science Diet i/d which may help or one of the diets for food allergy or intolerance. Also, a low carbohydrate diet might help.
There is a medication which combines simethicone and activated charcoal called ‘Flatulex’ which may help and which is available for people and can be used for cats. It can be bought over the counter. It should not be given to cats with liver or kidney problems.
Overweight cats are more likely to suffer from flatulence and gradual weight loss might be called for by a reduced diet and some exercise.
