Re eating sick animals.
1) if you read any of the good books there are instructions about only eating animals that are healthy at the time of slaughter and don’t eat anything that you don’t know how it was killed. There are also instructions on time of year, temperature etc. some animals - pigs in particular are really singled out as somewhat challenging. Pigs are often full of worms and other parasites. These instructions were written down thousands of years ago and are still valid today. Indeed our best practice guides are just a modern interpretation.
2) animal physiology- all animals have evolved a pretty good physiology to keep out pathogens- our skin and digestive tract / lungs are a pretty effective barrier to bugs. Stomachs contain acids and enzymes that break down cellular structures from food, animal and / or plant, releasing all the nutrients. In most cases there are then lots of microbes in the intestines which thrive on the broken down particles and break them down further. Those microbes are then also broken down and nutrients are adsorbed. In ruminants, deer, cattle, sheep etc the Rumen acts as an initial fermentation/ digestive vat. Grass / leaves etc are pretty poor nutrition for an animal. A ruminant has evolved so that it fills the rumen, this is full of fungi and other microbes which feed on the cellulose and nitrogen in all the vegetable matter, and grow rapidly. These microbes then slop over into the true stomach where they are then digested. In animals such as horses, elephants, rodents etc can only rely on secondary digestion from microbes in the hind gut. This is very much less efficient and its why a horse needs three or four times the amount of fodder as a cow to put on a kg of meat.
But I digress. Pretty much any microbes and bugs will be digested and broken down in the digestive system.
With the lungs, there is a very effective mucous lining with finger like villae that effectively trap any bugs and dust and walk this up the lungs to the top of the digestive tract where the snot is the swallowed and digested.
As we get older these systems break down. In particular the lungs ability to trap and transport out bugs is badly affected by smoke and pollution. Smoking / exhaust fumes don’t kill directly, they kill by buggering up the ability to control infection.
the digestive system, if it is exposed to unusual/ harmful bugs has a very effective way of expelling such bugs. It’s why we tend to explode if you change your diet, go to a different country etc. same with animals.
Fundamentally though animals are pretty good at avoiding infection.
3) preserving and cooking. Most bugs don’t survive very well in extremes of temperature, or in very dry, salty, acidic or sugary conditions. Mankind has developed many different ways of preserving food and killing pathogens before the are eaten.
The most important is cooking, and if you cook meat properly you will kill most pathogens.
However warming meat up to natural body heat - a bit above 30°c just makes them vigorously multiply. One of the real challenges with slow cookers or water bath type cooking is that temperatures may never get high enough to kill the bugs. Put a stew in the oven or on the stove, at the least the liquid on the interface between the pot will get to a high heat for a few seconds before it then goes into the rest of the stew. Temperature in the centre of a steam bubble will be well above 100°c.