Normally when a size one city creates a settler, the city disbands, something you probably want to avoid. But it does NOT disband if it is your ONLY city*. It does not lose any food from its foodbox either.
This is a great trick to use when you start a game with only one settler. Found a city, and place the worker on a high-shield tile such as forest. Make a settler in about 12-15 turns. Then your city grows to size two (this may occur within just a few turns if you've played around with the workers creatively). Then you can make another settler quickly, with a nice start to your game. Variations are possible (making two settlers from the size one, etc) but they are less useful IMO.
* I may be forgetting other requirements/details. Not sure if the city has to be your capital (but in practice it always is). Also, not sure what happens at chieftain level (IIRC cities never disband there?).