Animals can live a surprising amount of time with a permanent hole to their stomach, especially if it is a surgically made fistula. Humans have had fistulas; the first human on record as having one was a French Canadian by the name of Alexis St. Martin. He sustained a life-threatening musket wound in 1822, and was marked a terminal case by his physician. However, he managed to heal and was mostly functional again within two years - except for a hole in his stomach that would never close. Through this hole doctors were able to examine inner workings of his stomach.
Nowadays, agricultural scientists learn about the digestive system of cattle by putting holes in cows - and the cows stay alive and well. These cows (fitted with a sealing cover called a "cannula") each have a hole into their stomach. Through this hole one can extract food caught mid-stream through the digestive system.
Fistulated cows are used to research the digestibility of different foodstuffs for cattle. One can feed the cow, then later catch the food while it's digesting to see how it's doing. Without fistulated cows, one would have to look at external factors in order to garner information about the best food for cows - none of which are as accurate as food sampled right from the stomach. Since cattle is such an important part of life (for milk and beef), it is important to feed them well.
Do not worry too much about negative effects of fistulation on the cow: the operation does not cause the cow any pain, and even prolongs the lifespan of cows. A fistulated cow that grows sick to its stomach can have helping substances put in directly. Plus, a single fistulated cow benefits livestock all over the world.
One could understand how some people might get upset based on a fistulated cow's alternate purpose - entertainment. Occasionally scientists will let people stick their hands inside of the cow to see what it is like. So, if you ever find yourself wondering what the inside of a cow is like, make friends with someone at an agricultural university.