Yup; I’ve had them. smelly white things that come out from the back of the throat, they look hard but then you can smoosh them.. they’re called tonsil stones or tonsiloliths.
Tonsils are located in pockets at the back of the throat; sometimes debris get stuck around the tonsils in the pockets and grow, like pearls do, slowly with other stuff get stuck to them.. And of course some of those stuff are food particles and bacteria, hence the smell. This tends to happen more often in people who get tonsillitis or inflammation of their tonsils of course.
If this is something that’s quite bothersome, in that it causes bad breath sometimes or difficulty swallowing (depending on the size of the stones) and sometimes sore throat.
To address them, there is a range of treatments, from gargling with saltwater or dislodging the stones manually with a pick or a swab, to antibiotics or in extreme cases removing the tonsils or the deep folds at the back of the throat.