I do not know Illinois real estate law (disclaimer).
The purchase contract should stipulate both parties obligations.
In California the standard residential purchase agreement provides the buyer with an inspection (contingency) period. At the end of that period, all contingencies (loan approval, appraisal, inspections) need to be completed, then a Removal of Contingencies form is signed by the buyers, releasing the contingencies. It is possible not to release all of them.
When an issue arises from an inspection (which is common), the buyer issues a Request For Repair, which the seller can either agree, disagree, or offer a compromise. Then the buyer has to agree, disagree, or counter propose another solution.
Normally, in the real world of people, not legal forms, the two Realtors representing both parties are talking on the phone or via email about the negotiations. In other words, if the buyers want a lot of repairs completed (more than the seller is probably willing to do), you have a classic case of Realtors negotiating on their client's behalf.
Buyer's Realtor: "The buyers were really disappointed with the inspection report because the house looks great, but there are some serious problems the inspector found. The electrical system is 50 years old and the entire thing needs to be replaced".
Seller's Realtor "I am sorry that your buyers are disappointed. Most homes in this area were built in the 1940s and 50s, so their electic systems are old, but they still meet code. Are you saying that the buyers won't proceed unless the entire electrical system is replaced?"
Buyer's Realtor "No, but they are concerned about buying a home with an old, outdated electrical system and would feel more comfortable with a new one"
Seller's Realtor, "If the system was not up to code I think you'd have a case, but as it is as long as the system passes inspection I cannot talk the seller into spending thousands of dollars on a new one. So if the seller repairs the garbage disposal and the sprinklers, are your buyers okay with proceeding?"
Just to give you an idea...the two Realtors would know if there was a material issue (one that would cause the buyers to cancel the purchase) far before the paperwork stage. In the above case it is common to have conversations, then then buyer's Realtor would discuss with their clients regarding how they would like to proceed. Some buyers think that they deserve a entirely rebuilt home, and most sellers are not going to agree to that.
So in California if a buyer had submitted a request for repairs, then the seller responded, there would still be an inspection contingency that needed to be removed. At the 24 hour mark, if I had not spoken to the other agent, or heard from them, I would draw up a cancellation notice, that the seller would sign saying if the buyers do not remove the inspection contingency the escrow is cancelled. This is an extreme step and would only occur if there was no communication from the buyer's Realtor.
In California if the seller does not sent a notice to the buyer about the contingency, then the escrow can proceed with the contingencies never removed. That would mean that at anytime the buyer could cancel by saying, "you didin't fix it". So as long as the buyers have not removed the contingencies, it would seem pointless to proceed with the escrow until the issue is resolved. If you goal is to get the home sold, then I would focus on finding out the problem and resolving it. If you are unable to contact them, then cancelling the escrow is the best option, because you want to re-market the property and get it sold, instead of holding out hope that they will eventually close. The real job of Realtors is in the escrow process, helping the parties to get to the closing table.
Hope this is helpful.