She's been dealing with gerd and food getting stuck in her throat so she hasn't eaten anything solid for over a week now. She's going to be going in for a test for her throat soon. Couldn't taking a stool softner dehydrate her? What is in her that needs softing if she hasn't eaten?

My 93-year-old mil went through something like this and was given gel-like substances to "eat." Can your grandmother drink liquids? Ensure or Boost would be good to give her. When is the doctor appointment? Why does she want a stool softener? Is she uncomfortable?

Stool softeners are very mild. I'd give her what she wants. She may have constipation if there is no motility in her gut, either from old age or from lack of fiber. She may 'feel' constipated and might very well be. It could even be from before her liquid diet.
Antacids are constipating, if they are calcium carbonate based.
Not being able to swallow is very common as we age. She may have to adjust to it permanently, by adjusting how she takes her food. Time for a blender/food processor to get creative and add enough liquid to everything. Talk to the doctor too about alternatives to pills, or get a pill cutter for the solid ones. They are often put in a spoonful of applesauce.
(Apples act as stool softeners for me - apple pie especially.. )