I sold my last mini van about 9 years ago in a similar fashion. The buyer never took the title to the DMV and he installed license plates from another vehicle on my van for his elderly mother to use (illegal, maybe not insured??). Much to my surprise, when she tried to sell it a few years later, it turned out that is still showed up at the DMV under my name. I got everything straightened out and a lawyer I contacted said that if something had happened during this time I would have not been liable (I had a sales receipt). Still, it caused me some anxiety.
I would never do that again for liability reasons. Call your DMV and get advice.
Illinois has a form you can have the buyer sign that indicates they bought the vehicle. When I sold my 1999 Grand Marquis last fall, I created a bill of sale, signed the title and had the buyer sign the form as well.
I believe there is also a little tear off "coupon" on the title where you can let the state know the name and address of the new owner. The new owner doesn't sign it, so it's up to the seller to collect that info and send it to the state. It has a barcode, so I suspect they might machine read it to flag the title/VIN/registration or whatever they might do.
It must work as after I sent this information to Springfield, they did not send me a renewal notice for my tags.
Of course, I also collected my tags, kept any registration, etc.
I provided the buyer a copy of the BoS, the signed over title, and a copy of VSD-703. I had it all printed up and ready to go and had the buyer sign as I counted the cash. Once I was satisfied, I handed over the title, the keys and wished him well.
Edited to add, my BoS form records mileage info, VIN, indicates the purchase is AS-IS, no warranties expressed nor implied, that the buyer has had opportunity to have the vehicle professionally inspected at his/her costs, etc. All manner of CYA stuff in case they want to come back and complain.
Never had a come back yet.