When you get an organ transplant your old organ will be sent off to a lab where they may want to analyze the old organ.
Then after they get done analyzing the old organ the lab or hospital will likely incinerate the old organ that was remove from you.
You can usually keep your old organs as well as some people have done so.
Just let the doctor know that you want to keep your old organs and they may let you keep the old organs.
But if you don't keep the old organ then it will be destroyed.
The old organ is considered to be hazard medical waste and will be handled carefully and destroyed.