From Anne Frank's diary, we know their food wasn't the best. She wrote about how, "In the twenty-one months we've lived here, we've been through a good many "food cycles" -- you'll understand what that means in a moment. A "food cycle" is a period in which we have only one particular dish or type of vegetable to eat. For a long time we ate nothing but endive. Endive with sand, endive without sand, endive with mashed potatoes, endive-and-mashed potato casserole. Then it was spinach, followed by kohlrabi, salsify, cucumbers, tomatoes, sauerkraut, etc., etc." The German government implemented rationing in 1941 and first applied it to bread, flour, cereal, pasta, butter, margarine, vegetable oil, meat, fish, sugar and confectionery all across the country. My best guess would be that they were largely fed from gardens that were grown by the people hiding them since plants and vegetables weren't nessisarily rationed by the government and would be harder to get caught for, as opposed to stealing extra meat or bread.