- To prevent infection in dead people. Couldn't have that...
- In cause the person giving the shot pricks himself.
- In case the prisoner receives clemency after the needle is inserted but before the drug is administered.
- Etc., etc.
But I think people actually do wonder about this sometimes, so I'll answer the question - once and for all.
Doctors don't sterilise any needles. All the needles that we buy are already sterilised during the manufacturing process, presumably on the assumption that we aren't going to use them to murder someone.