Yes, iron nails rust in anhydrous calcium chloride due to a process called deliquescence. Anhydrous calcium chloride is a highly hygroscopic substance which means it has a strong affinity for water molecules. When exposed to the atmosphere, it absorbs moisture from the air and becomes a liquid solution.

The presence of water in this solution facilitates the process of oxidation of iron present in the nail. Oxygen from the air reacts with the iron in the presence of water and moisture, forming iron oxide, commonly known as rust. Additionally, calcium chloride acts as a catalyst, accelerating the corrosion process and intensifying the rusting of the nail.