Fish will probably not do much if they get too cold, so yes, they would probably be motionless just lying around. Since I've never frozen one of my Oscars to death, I couldn't tell you at what temperature an Oscar will die. However, I shouldn't let the temperature get below 20°C for too long. 16°C is a little bit too low and I think the fish would be stressed if the conditions were like this for any period of time.
Even though fish don't show signs of stress, they still can be stressed. When fish get stressed, it can increase the chances of them developing disease such as White spot, or even worse, hole in the head disease. Unfortunately, there's not much you can do if you've got a problem with heat. This is why I like to keep my water temperature at around 28°C. If the power does go off, you've got a little bit of time before the temperature drops too low
I would advise you to get a heater in your tank, 21°C is the absolute minimum I would like my temperature to stay at. Even then, you might have other fish that can't tolerate a temperature that low.