You don't have to die in a hospital to donate your organs.
When you die you can donate any of your organs that you want to donate no matter how you die.
As long as you're in good health and have no diseases that could affect the donated organs the organs can be donated whether you die at home, in the hospital, nursing home, car wreck, murdered etc.
There's no requirement for you to die in the hospital for your organs to be removed from your body and then donated and transplanted to someone else in a hospital.
When you die they can take you to a morgue where they can open up your body and then remove the organs that they can still use.
Many people donate organs whether they die in the hospital or die by murder, accidents, car wrecks, die at home etc.