There’s quite a lot of people interested in fasting for spiritual and health purposes. When fasting, these people don’t drink anything but water and don’t eat anything at all, their stomach simply pauses. And it’s not unusual to fast like this for several days or even weeks.
One of my friends tried a three-week fast and I happened to meet him just as he was ending. He was quite skinny, but appeared fully functional. Another friend of mine fastened for at least two weeks, I can’t remember the exact number. Both of them lead a normal life, the first one even kept running his usual kilometers and the second one kept working as a scientist.
I am not saying that you should try this or that it’s completely harmless. (Especially the return to normal food takes a long time and you must excercise a great care and discipline.) My point is that three weeks without food is nothing unheard of and you don’t have to be a walking corpse in the end.
I’m not sure if eating small amounts of food is better than eating nothing. During the first several days of fasting the body shifts to a different energy source, it could be that starting the stomach again would do more harm then good.
Anyway, if you happen to be without food for a week or so, there’s no need to panic. You’ll be uncomfortable, but you’ll be fine. You can even try fasting for several days to see how the body works in those conditions, but in that case please don’t trust a random stranger on the Internet and find somebody who knows what he’s doing :)