Asset Sale and Union Obligations - If Only the Seller Is Unionized, Must I Recognize the Union?

I am in the process of purchasing a business in Illinois through an asset sale. The current owner is union-affiliated but will be leaving the company as part of the sale. The employees who will continue working with the company post-sale are not union members. Since this is an asset sale, am I correct that I would not be required to recognize or negotiate with the union representing the former owner, since none of the remaining employees are unionized? Are there any common issues or pitfalls buyers face in these situations? Any insights or real-world experiences would be helpful. Thank you!