Legal Question in Real Estate Law in Illinois

Anything can happen, including a closing. Without seeing the contract, however, it is impossible to be absolute in terms of a response. However, what seems to be the case is a survey defect (encroachment of a portion of a permanent structure on the property you want to buy onto a neighbor's property). It may already be in 'chain of title' or may be in a prior title insurance policy. Or it may be newly discovered. If the title insurance company is unwilling to issue what is called an 'encroachment endorsement' (ie they will take the risk that at a future date the neighbor might attempt to make you remove the encroaching portion), you have a problem. The contract should specify how much time the seller has to take care of this situation and then what your rights as buyer are if seller can't. There are various factors involved, by the way, such as whether this is the main structure (house, etc.) or it's an outbuilding (garage, shed....) so your information is also incomplete, making an answer that much more difficult to give.