This happened to me once. But it is a pity that you don't get an option to keep the kid in your game. Just a pop-up window asking you if you'd like to move the kid to another household would suffice.
It never happened (as far as I can remember) to an active household in my game but I wonder what happens then. Say for example you are playing a single mother with her kid and she dies because she didn't clean the lint tray from the dryer. What happens to that kid? Do they just disappear and you get send into the world map?