I've seen televisions have that issue. They can come back on in the middle of the night. To me, this makes sense for a lightbulb. If your failsafe "backdoor" expects it to be wired to a switch, you would turn that switch off in the event of a power outage. What else would it do when the power comes back on?

One thing I really like about "smart" things, when the power is out at home I can check my phone to see if power is restored. I guess that's similar to calling your home to see if the answering machine is back on.