In Illinois is the surving spouse responsible for medical bills if their is no estate?

The base assumption is always going to be that that the other spouse inherits the other's assets. But the estate has to liquidate all assets before they can transfer them to the spouse. One way or another, the spouse ends up paying the debt. The spouse has some right in all real property owned by the husband. If the assets are not enough to cover the debt, the real property may have a lien placed against it to cover those debts.