Under the Illinois Probate Act, 755 ILCS 5/2-1(a), if a spouse dies with no will (intestate), the estate is divided 50% to the surviving spouse and 50% to his children in equal shares.
Anything held jointly will automatically pass to the surviving spouse, so anything held in both their names will become hers.
This is the law
Sec. 2-1. Rules of descent and distribution. The intestate real and personal estate of a resident decedent and the intestate real estate in this State of a nonresident decedent, after all just claims against his estate are fully paid, descends and shall be distributed as follows:
(a) If there is a surviving spouse and also a descendant of the decedent: 1/2 of the entire estate to the surviving spouse and 1/2 to the decedent's descendants per stirpes.