I don't lnow if you still need an answer, but basically if she stops her insulin, her sugar will run extremely high, and her organs will begin to break down. Her nerve endings will get damaged and over time and as a result she could go blind, have terrible pain in her limbs-and even might have to have them amputated. These are only some of the things that can happen to a Diabetic who doesn't take care of themselves(kidney failure, heart disease, neuropathy..) The process is slow, but overall unreversable once the damage is done, as far as I know. She could also go in to diabetic ketoacidosis and begin losing weight very rapidly, and also risk going in to a coma beacause of the extrememly high sugar level.
I have Type one diabetes, maybe your sister is doing this or saying she's going to do it as a cry for help...someone to pay attention and find out what is really going on. It could be the disease thats making her depressed, or something else entirely. How old is she?