What causes these stenches/odors from a cat?

So I just recently gave these pills to these cats for my neighbor. She specificed them having worms, but she wasn’t so sure. I was focusing on this other cat of hers, it was approx. 12 years of age, just skin and bones, it had a foul smell/odor right when your near it, and could possibly smell it a foot away. She wasn’t an easy target when giving the pill(Though I’m not an expert, but with the treats they gave us wasn’t accurate, so I was already known how to give the pills) This cat, as I said was just skin and bones, the fur was rough as if someone shaved her, and her fur was very thin and missing as if she had spots. Her breath was also an issue when I opened her mouth and dropped the pill I wanted to gag at the stench :l She also would be laying at different areas of the house and would leave behnd small redish brown spots like flea droppings or something releasing from her fur. Could someone provide me some links or at least tell me what to do and if it’s an option that she could be put to sleep. Our neighbor is really worried. Note: The cat drinks a lot of water daily, always goes to the food/water and just eats/drinks, and tends to lay somewhere where it’s cool.