Hibernation

[Mrzocor 0]

Does ESET continue to protect your computer even when my computer is in hibernation mode?

[Super_Spartan 56]

Hibernation means the computer is fully shutdown albeit the current state is saved to the hiberfile.sys so when you startup your  computer, everything that you had opened is still there as if you didn't shutdown. So ESET has nothing to do with that and it certainly won't do anything when the computer is hibernated, it's fully OFF anyway