A few states have enacted laws that require an auto repair shop to offer to return the parts taken out of your car. As far as I can tell, IL is not one of those states. You can see a summary of the IL auto repair law on the IL Attorney General’s web site at:
As a result, if you want the old converter back, make that clear before you give the shop the car for the repair and ensure that the return of the old converter is written in the invoice or contract you receive. That will eliminate fights over this later. The usual custom in the auto repair business in every place I've lived is that the shop keeps the old part, in part because non working parts are not worth much, if anything and car owners do not want them back. Thus, the shop disposes of the parts for the customer. As a result, absent some agreement to the contrary upfront, I rather doubt you can claim the auto shop stole the part if it does not return it to you. So, get the shop to agree to it upfront (or give you an appropriate discount to reflect it's value) or go someplace else.