What happens to boiled (BMIM)PF6?
Ionic liquids are not magical liquids. They are just typical organic compounds with certain properties. These compounds generated a storm in the tea cup in the late 1990s and 2000s, but they are as toxic as other solvents. Certainly they have niche applications especially as a gas chromatography stationary phase, where they can be used at high temperature (up to 350 centigrade!).
Now you can guess based on the GC application, that ionic liquids cannot be distilled or vaporized. They start to decompose by complex path ways above these temperatures. We can easily see that in a gas chromatograph. Surprisingly, not much has been studied as what happens to ILs at high temperatures.
Only one recent study exists Dicationic ionic liquid thermal decomposition pathways. There are complex decomposition products in the absence of oxygen. Like any organic compound, they will burn in the presence of air. NaCl is another story. It is not an organic compound. In short do not compare NaCl with ionic liquids.