Consider a embedded system such as Electro Hydraulic Power Steering ECU mounted in a heavy duty commercial truck.

When key switch is turned off, the ECU should executes very limited functionality in sleep. It is not suppose to log faults in sleep mode?

 

What exactly (what, why, how and when) does logging mean? Something that's critical could wake the controller (using a interrupt or polling process) for logging if that's a system requirement.

 

There is no rule. Since you are designing it, the decision is up to your discretion.