Pharynx with blocked trachea
You can see in this case, that the epiglottis failed to cover the trachea while this person was swallowing, and as a result, the meat lodged within the airway.
The epiglottis is elastic cartilage, and is a fairy stiff structure. Just like every other thing ingested, foods like meats (which are dense and generally not easily broken apart, even after chewing) can end up getting into the trachea if the epiglottis does not function correctly. However, it’s noted in this book that they can be more difficult to dislodge than other foods of comparable size, simply because they’re able to get “caught” on the epiglottis. An emergency tracheotomy is generally the only hope those patients have, as forceps or other medical tools are needed to dislodge the meat, and most people don’t carry those around in their pockets…
A Text-Book of Pathology. W. G. MacCallum, 1916.