Kidneys on dialysis. Many people on dialysis maintain some level of residual kidney function. This is especially true for peritoneal dialysis. This residual function can make a huge difference in blood pressure management, and also in general health and mortality, so it is important to try to maintain it by avoiding kidney toxins (including medicines) and controlling blood sugar, and salt and phosphorus in the diet.
Maybe. With kidney failure requiring dialysis, the problem is that the "nephrons" in the kidney do not filter the poisons from the blood. While kidney failure may be due to complete lack of blood flow to the kidneys, in most cases the arteries remain open and some blood passes thru the kidney organ, it is just not able to be filtered.