No your body won't just shut down and you won't lose anything. Think about it. If that was true, people would never starve to death! But, in fact, they do.
My understanding, however, is that if you eat very low calories your metabolism may slow somewhat. You would still lose weight though. If someone is really and truly eating 950 calories a day, each and every day, and never eating more than that and is a normal person without illness who moves around normally during the day -- that person will lose weight.
So one of these things is most likely to be true if someone actually does think their body has shut down due to eating low calorie (I'm not saying this is actually your situation, just responding to the point):
1. The person is eating more than they think they are. Most people are very inaccurate at estimating calories eaten. Have they been weighing all their food and recording all of it immediately upon eating? If not, try doing that for awhile.
2. Sometimes people don't recognize the impact of 1 or 2 high calorie days. They eat 950 calories most days but then have a day they eat 2500 calories. They have to count those extra calories.
3. If really and truly eating 950 calories each and every day and they aren't losing weight - then maybe they need to get checked out by a physician.
I like this article about Starvation Mode: