Is it safe to eat unrefrigerated foods?

It depends on what types of foods we are talking about. Rotis stay good for eight to ten hours and then start to dry up. I have seen many leave boiled rice unrefrigerated. In fact some say that it does not go bad for ten to twelve hours! I, personally, would be uncomfortable eating leftover food that has not been refrigerated within two hours of its cooking. This is true for home made food. Leftover restaurant food has to be refrigerated the moment you come home with the packets because we really do not know at what time the food preparation had started. Keeping cooked food out allows microorganisms to live, grow, and multiply. For example, bacterial growth is ripe between 4.4 - 60°C. Bacteria reproduce rapidly at room temperature or even lower (20°C), some forming toxins that can make you quite ill. Keep the following in mind so that you can enjoy your food safely. 

After cooking, your best bet is to place food in shallow containers. This allows the food to cool down more quickly. Be sure to refrigerate promptly between 1.1 - 3.9°C. When you reheat leftovers, they need to reach 73.9°C or be steamy hot all the way through. For dals and soups bring them to a full boil. Storage times for properly refrigerated foods vary, but generally use leftovers within one to two days. 

Never taste food that looks or smells strange or unusual. Go by this rule: If in doubt, throw it out!