Cats can eat one egg a day. Feeding eggs to cats may cause diarrhea. Closely observe your cat's bowel movements after feeding; if any abnormalities are observed, stop feeding eggs. Eggs are rich in nutrients, especially protein and lecithin, but they also contain relatively high levels of cholesterol. It's recommended to feed them eggs in moderation. If your cat is obese, it's not advisable to feed them eggs. 
Benefits of cats eating eggs:
1. Eggs are nutritionally complete, with amino acid and trace element content that almost meets the gold standard required by animals.
2. The lecithin in egg yolks can make a cat's fur softer.
3. The lecithin in egg yolks is also a fat emulsifier, which can emulsify the fat in the fur and help cats expel hairballs from their stomachs.
4. The high fat content in eggs also makes them more palatable to cats, stimulating their appetite.