I think it's most likely that it would just get buried or piled up somewhere. Salt is not really a high value product, so I wouldn't be surprised if desal plants had to pay people to take the salt from them.
* Problem 2: If dumped into the ocean, it increases the salt concentration (see: Middle East).
Disclaimer: Worked on some related projects on how to find a positive use for Brine.
The scale is the problem. At the end, you still end up with lots and lots of inorganic material, which is toxic for the environment.
But there's also industry that extracts the salt from the Great Salt Lake, via evaporation. This shows that, if you've got salt to dump somewhere, there's actually a market for that. (That is, if it's pure. Others pointed out the problem of chemicals added to the salt water to make it easier to process.)