Hard boiled eggs do eventually go bad.
When you hard boil the egg the egg goes bad faster than it would if it were fresh and not hard boiled.
If you hard boil eggs you need to make sure to keep them in the refrigerator and when kept in the refrigerator the hard boiled eggs should last from 10 to 12 days before they go bad.
It's best to eat the hard boiled eggs within a few days to 7 days of refrigerating them but I have eaten hard boiled eggs that were 10 days old and they were just fine.
Hard boiled eggs can be eaten after 10 days as long as the hard boiled eggs have remained refrigerated for those 10 days.
Also make sure the hard boiled egg still smells good and if the hard boiled egg smells good then it's safe to eat and should not harm you.
Or if the hard boiled egg smells bad or has a bad taste to it then throw it out as it could make you sick.
I have eaten hard boiled eggs that I've had in the refrigerator for 10 days and never got sick from it.
But I made sure to smell it first and see if it were still good.
If you leave the hard boiled egg out at room temperature too long then they can go bad quicker but the refrigerator keeps some bacteria from growing so fast on the eggs.