Never put eggs inside the microwave. They can shatter because of internal steam pressure building.
Now you told them not to do something, you know they are now going to try it, in fact they probably already will have before you post again..
If your going to try it use a Pyrex bowl over the egg it's a lot easier to clean afterwards, and if anyone uses my microwave they better get ready for the size 13 steel toe to the rear, yes I hate messes in my coffee re-heater, but metal spoons in a cup of coffee is ok with me and so are frozen juice cans with metal ends so long as pop the top..
In those cases the Magnetron's output power stays the same i assume. Where it goes then ? (or where the power goes when i run the oven empty etc) ?
If there is no load it will discharge in the air and off the insides of the microwave, basically it's shorting out generally it's not the best idea to run a microwave with no load inside it for an extended period, and can result in the burning of the mica window just outside the magnatron waveguide, allowing food splatter or egg explosion to get in and then you'll smell burnt food for weeks ...