A firearms manufacturer can have full autos in Ill. There's a guy just outside of town who has a collection of them.
Do you really think your answer applies to the OP's question?
As a LEO I could possess full auto weapons. When I was in the military I could possess full auto in IL. Neither of which has any relevance to the OP's question. There are all kinds of exceptions in the statutes which we could cite altho none of them would be relevant.
No fully automatics ANYWHERE.