When a party dies without a will, this is called "intestate" and the property passes via the laws of intestate succession, in most instances. Exceptions to this would include the following:
property held in joint tenancy with right of survivorship;
pay on death/transfer on death bank and brokerage accounts;
life insurance proceeds payable to a beneficiary.
In those instances, the property passes by operation of law to the named individual.
For other property not addressed in a will, the property passes according to the statutory "next of kin" as detailed in the relevant intestate succession statute.
According to the laws of intestate succession in IL, when there is a surviving spouse and descendants (ie children) of the decedent, the surviving spouse inherits 1/2 of the property that goes via the laws of intestate succession, and the children would inherit the other 1/2.
That statute is accessible here
All estates require probate (unless there is a trust, and all the property passed via the trust; then the trustee administers the estate).
In IL, there is a small estate procedure for estates under $100,000. All probate filings are public record, so the heirs can contact the court clerk and obtain a copy of any probate filings to date.