The hub stops working, which means anything that needs to go through the hub will stop working. Which means almost everything.
It would be possible to set up a Z wave battery operated motion sensor to trigger a Z wave battery operated siren, but that’s about it as far as useful stuff if you have no power. Because of course all of your plug-in devices will also stop working whether they integrate with SmartThings or not. 
There are some community members who have back up power supplies for their Internet router and their smartthings hub, and you could do that. But if the power is out in the rest of your house it won’t do you much good.
Since this thread is about the V3 hub, it’s important to note that This is very different than the ADT/smartthings security panel model, which does have emergency back up options. So if you are looking for a security system, I would definitely choose the ADT/smartthings model over the V3 hub model.
There are some additional discussions in the following thread but as far as the V3 hub, essentially if the power is out, the power is out. Your battery powered sensors might continue to detect something, but you won’t get any notifications and none of your automations will work.