Some foods do in fact contain no protein at all. But in reality, it is virtually impossible to find a well-balanced diet that does not contain some trace amounts of protein. While identifying foods with little to no protein may help people who need to watch their protein intake, it is not recommended as a repetitive eating habit or lifestyle.
There is no such thing as a no-protein diet. Protein can never be completely eliminated from the diet without dire health consequences. Protein is found in trace amounts in even the most non-protein food sources.
Non-protein foods, or food with trace amounts of protein, are sugars, fats such as butter, and fruits. Foods with very low amounts of protein include vegetables and starches such as bread and pasta.
People with certain diseases of the kidney or liver need to follow a low-protein diet because excess levels or even normal levels of protein can greatly interfere with the normal function of these organs.
The average person needs to consume at least 40g of protein per day to maintain good health. A diet that consists solely of sugars and fats can cause a several adverse health effects, from obesity to diabetes to impaired organ function.
Plant-based or vegetarian diets can in fact contain large amounts of proteins because many plant-based foods are significant sources of protein, such as beans and quinoa.