It is not safe to eat boiled eggs that are left out overnight as they can spoil and grow bacteria.
Boiled eggs are considered safe to eat when left out up to 2 hours.
If the boiled eggs are left out longer than 2 hours they can grow bacteria could make you sick so it's not recommended to eat boiled eggs left out overnight.
While I have eaten hard boiled eggs left out overnight before and never gotten sick I don't make it a habit as it could make you sick.
So while you could eat hard boiled eggs left out overnight and may not get sick you would do so at your own risk.
Always refrigerate any hard boiled eggs if not consuming them within a few hours.
The hard boiled eggs left in the shell are less likely to grow bacteria if left out overnight but they still can.
If you do eat a hard boiled egg left out overnight make sure it smells good and does not look bad.
It's safer to throw the boiled egg out if left at room temperature longer than a couple of hours to avoid any potential foodborne illnesses or food poisoning.
But many people have safely eaten hard boiled eggs left out longer than a few hours and even overnight but it's at your own risk.