It would be way riskier and more expensive to donate insulin than it is to make insulin from slaughtered animals, which is still done in some parts of the world, or from genetically engineered yeasts and bacteria (which is how all of the insulin for sale in the US is made).
After you die, your pancreas can be transplanted into another person and make insulin for them. About 1000 pancreas transplants are done in the US each year (that's about 1 in 500 type 1 diabetics getting a pancreas each year). It's risky because the person has to take transplant medications, and the transplanted pancreas usually only works for a few years, but in some cases it is worthwhile.
Some partial pancreas transplants, where a part of a living person's pancreas was given to another person, have been done with some success, but they aren't being performed anymore in the US- I'm not sure why not.