Eating stale food is usually safe and okay as long as the stale food has not actually spoiled.
If you eat stale bread, stale crackers, stale chips or other stale foods that are not meat products then it would likely not make you sick.
Although you might get a stomach ache from it.
Stale meat though could actually have bad bacteria in it and should be thrown out as stale meat could possibly make you sick.
That is unless the stale meat has been frozen all the time then it's okay to eat.
Rancid food is usually not dangerous to consume unless it has actually spoiled enough to have bacteria growing in the food.
It's still not a good idea to risk your health when eating rancid food and it's better to throw the rancid food away and eat fresh food to avoid getting sick.
Rancid food is food that has bad smells to it or bad tastes to the food and the food is unpleasant as a result of being old and stale.
Rancidification of the food is the process of complete or incomplete oxidation or hydrolysis of fats and oils when exposed to air, light, or moisture or by bacterial action, resulting in unpleasant taste and odor.
Eating rancid food can make you sick to your stomach and cause vomiting, abdominal pain, bloating etc.
In rare cases the rancid food when eaten may lead to food poisoning if it has bad bacteria in it.
If you eat rancid food you won't get deathly sick but you may have stomach problems and other digestive issues.
When food goes rancid the food develops new molecules that form as oxidation occurs and that may lead to digestive issues.
I would not personally eat any rancid food though because although most times rancid food is not gonna harm your health there is a slight possibility that the rancid food could have some bacteria in it that may cause food poisoning.
I would recommend throwing the rancid food out just to be safe but most times the rancid food will not hurt you as long as it's not too far advanced in the rancid department.
If in doubt you should throw spoiled food out because really it's not worth risking your health over even if it might be okay to eat.
Especially if the meat is rancid you should throw that out because rancid meats can lead to health issues and possible death.
Plus rancid or spoiled meat will smell so bad that you won't want to eat it anyway.