Is there any changes to the 'untransplanted' kidney in a kidney recipient ? is there any damage to that kidney when the other kidney is from a donor?

See details: I am not sure what you mean but if someone requires a kidney transplant that means that neither one of that person's own kidneys is functioning to an acceptable degree.

Natural course: After a kidney transplant, the new kidney takes over the missing function of the native kidneys and normalizes the renal function for the body. The old or native kidneys remain and gradually decline function as they were doing prior to transplant. The transplant does not cause any damage to the native kidneys nor accelerate their decline. It only adds better kidney function to avoid dialysis.