With renal failure does that mean the rest of my mom's organs will start shutting down?

Organ shut down: If your mother has end stage renal disease and is on chronic hemodialysis (d), the answer is no. If you mom has acute renal failure due to low blood pressure, there is a chance that she can develop multi-organ failure. You should ask her doctors that question, as they know her case better and can give you a more informed answer to your question.