Saving for an emergency to me is saving for a flat tire, car repair etc.

Saving for a transplant???????? uh no, a kidney transplant is approx $200,000 plus hospital costs, 3 months recovery etc. Total is approx $400,000. (kidney transplant is not even one of the more expensive transplants, I just used it as an example) I suggest you have good health insurance. However, if you do not have proper health insurance the best thing to do is have the transplant done at a county hospital for free. Even if you have to go to a regular hospital you can still have a transplant done but then you would need to go bankrupt if you do not have health insurance.

I really do not know anyone who would be able to save for something like that. I would NOT consider this as a saving for an emergency.