Here is the inside of a closet. The bottom has rotten wood, that was taken out, leave a gap at the bottom. Problem there is nothing to attach the new wood to? What would you do in this situation?

Is this from termite damage or wood rot or can't you tell? Hard to tell from this picture if any plate remains. Not many wall studs I can see. Regular wood should not contact a concrete floor as this appears to be. I would cut the visible stud to be 1 1/2" off the floor and install a piece of pressure treated 2X4 using construction adhesive to glue it in and then toenail the wall stud to the new plate. . Floor must be spotless before gluing. Then, floor base trim can be nailed to the 2X4.

Yes I was thinking a long those lines. Possibly liquid nail adhesive on the 2 x4 so the base trim can be attached. But should the trim also be glued to the 2x4. Hammer a finishing nail may loosen the glued 2x4

Sure, you can do that.