Brake Shoes sitting wrong
I am not a brake drum expert by any stretch of the imagination, but I can think of 3 things that could be happening here:
1- The piston on the wheel cylinder that pushes on that side of the brake shoe is seized internally, be it rust or something else, so it now cannot move an pick up the slack on that side.
2- The brake shoe runs on 3-4 raised ridges on the back of the backing plate, and the shoes have worn out the raised ridges they run on. They could have worn a ridge into the backing plate deep enough so that they can no longer move freely into place.
3- The brake strut bar is not letting the shoe fit correctly, it is somehow putting pressure on the shoe and not letting it sit where it should. Could be because the parking brake has to much tension on it.
Anyway you look at it you will need to probably disassemble it to check out what the issue is.