Starvation mode is not likely to be the culprit here. Yes, if you eat a really low amount of calories, your metabolism may slow down some so you don't lose the same weight as as you would have if your metabolism hadn't slowed down. However, it doesn't totally stop weight loss. If it did, people wouldn't die from starvation, but sometimes they actually do.
This is an article I liked on this subject:
AS far as exercise. Yes, sometimes you can build muscle if doing heavy exercise. But, if you have a calorie deficit you still will lose some weight.
From what the OP says there are two culprits that should be looked at.
First, I agree that she should check with a doctor. There may be something going on medically that is affecting the calories that she burns or otherwise has an impact on her weight loss.
Second, if it isn't that, then double check the counting of calories. If you eat out a lot or eat packaged foods or food cooked by someone else, sometimes it can be really hard to count calories.
It might help to post a day of food with your calorie counts to see if anyone can spot anything that might be wrong.