Yeah the dead sea is obviously insanely salty. I am originally Jordanian so been there a couple of times. It’s so salty that you will feel every small scratch on your body tingle or sting. You have to seriously avoid getting any water in your eyes or mouth because it’s extremely uncomfortable.
Depends on the material, how quickly the salt accumulated, how much salt was absorbed into the cells of the fabric, and how effectively the salt blocked other agents of decay. There is a special type of museum/archaeology person called a conservationist, who deals with stabilizing recovered materials like this so they stop decaying, and can be stored/displayed. You’d really have to ask one.
Speaking generally, salt water is a fairly major agent of decay for metals because it’s highly reactive, but a little less so for organics like wood and cloth. Plant fibers have dense cell walls that retain much of their shape even if the interior of the cells rot away. Often their major agents of decay are micro organisms, which cannot survive without oxygen, so if the salt accumulated quickly, and did not do to much damage of its own, the fabric might be fine underneath because oxygen was blocked. This is why wooden shipwrecks and their contents survive better when buried under the sand instead of upright in the water column. Its an anerobic environment. If the fabric is an animal fiber like wool, much will depend on how vulnerable it is to hydrolysis, and how quickly the salt accumulated.