Final answer:
Salmonellosis is the illness associated with undercooked shell eggs, caused by the Salmonella bacteria. Proper cooking is essential to prevent food poisoning from this bacterium.
Step-by-step explanation:
The illness that has been associated with undercooked shell eggs is Salmonellosis. This foodborne illness is caused by Salmonella bacteria, which can be found in a variety of foods including raw and undercooked meats, poultry, dairy products, and seafood. When eggs are not cooked properly, the bacteria can survive and cause an infection once consumed. It is important to ensure that eggs and other potential carriers of Salmonella are thoroughly cooked to prevent this type of food poisoning.