Will an iron nail sunk in a highly concentrated salt solution rust?
Rust is iron oxide, $(\ce{Fe2O3.nH2O})$

It forms from iron(III)hydroxide made when iron reacts with oxygen in the presence of water. The chemical reaction can be summarized as follows:

$\ce{4Fe(s) + 6H2O +3O2 -&gt;4Fe(OH)3(s)}$

Now, water 'naturally' contains some dissolved oxygen (8-14%), depending upon the source of the oxygen (photosynthesis from underwater plants, diffusion from the atmosphere) balanced against oxygen demands (such as fish breathing and decomposition of organic matter). The temperature of the water also affects the solubility of oxygen (gases are less soluble at higher temperatures).

The ocean (which is typically 3.5% salt) typically has 20% less dissolved oxygen in it than freshwater. This is because the water molecules are attracted to the dissolved ions from the salt (solvation), which has the tendency to decrease the weak affinity of non-polar oxygen molecules to water, thereby driving dissolved oxygen out. 

Now, the salinity of the Dead Sea is about 290 (that's 29% salt!), which is over 8 times the salinity of the ocean!  At such high levels of salinity, most of the oxygen is 'salted out' of the water, which means that the levels of dissolved oxygen are very low, especially below the surface, so an iron nail totally immersed in water with 29% sodium chloride (salt) will not rust.