That's funny that you think the cops would do that. They only enforce the laws that are convenient for them.
Same thing happened in New York when they banned "assault weapons" and many of the sheriffs also said they wouldn't enforce the ban. Vast non-compliance with the bans is what happened, and will continue to happen going forward.
There are lots of ways to hide guns. One person who is a legal gun owner who doesn't approve of the law can hide them for his friends. Do not assume Illinois is united on this, enough voters are to pass a law, but gun owners consider this a tyranny of the majority and are sticking together
In a lot of rural areas where guns are most common the police don't approve of the law. They won't ask for a warrant in the first place. If someone else asks for one they will give plenty of warning to the person to be searched - or they will just take the warrant and throw it away without searching. If forced to search they will ignore you moving guns past the front door when they knock, then when the door opens find no guns in plane sight in the front room and leave.
And then when there's yet another mass shooting they'll jump up and down about how we don't need new laws because the person was already legally barred from owning them and we just need to enforce the laws that are already on the books.
"Cool, then you shouldn't mind if we search your entire property right now to prove that you don't still have the thing you are explicitly prohibited from possessing. Or you can show us where you were boating when they were lost and we can charge you for the cost of the search if they aren't there."
Make it clear to the rest that they need to surrender their illegal firearms.
So when do the SWAT teams and National Guard roll into the seedy side of Chicago to do this to the Gang Members that are carting around illegal firearms? When the hell are Illinois Prosecutors going to start jailing the people that police catch with illegal machine guns?
That person at home who shouldn't have a firearm is a a problem but they are far and away not the biggest problem and its not even close.