I'm sorry for your loss.
Depending on the circumstances, it is possible that the estate will need to go through some sort of probate. If a probate is opened, it will need to be filed in the city/county where your FIL lived in Illinois.
Probate is a process wherein a court receives the decedent's assets and then passes them along according to a will or the laws of intestacy. When a person dies without a will, it's called intestate. Here's a link to a the statute setting forth the rules of intestacy in Illinois:http://illinois-attorney.com/intest.htm
This statute is actually pretty straight forward and sets forth the various possibilities for what will happen. If the decedent had a living spouse, the spouse receives half of the estate and the decedent's children receive the other half "per stirpes." If there is no living spouse, the estate goes to the children "per stirpes". Per stirpes means that it is split equally among the heirs.
I am an attorney and I have done some probate work, but not in Illinois, so I don't know the specifics about probate laws there. I did google for Illinois probate information and found quite a bit of good stuff. Increasingly, law firms are putting such information on their websites and it's usually accurate. This site discusses whether a probate is necessary:http://illinois-attorney.com/lp10.htm
Apparently under Illinois law (and in the state where I live), a formal probate is not necessary if the assets of the estate are under $50,000. Instead, an interested party (one of the heirs) can file an affidavit stating that the estate is less than $50,000 and that it will be distributed according to the laws of intestacy.
The person who would file this document is similar to what's called a personal representative or executor in a formal probate. Generally, it is one of the heirs who is trusted to make the correct decisions regarding the trust and treat all other heirs fairly. In your situation, if your FIL has children living in Illinois, it would probably be easier for them to deal with the probate because they will be able to take care of things in person.
I think the biggest question here is whether you need to retain an attorney to handle this. Most of the websites you'll find about probate are from attorneys and (surprise) recommend hiring one. If the estate is under $50,000, you may not need to hire one because you can use the small estate affidavit process. However, this requires that there be an heir that everyone trusts to make sure that everyone gets their share and that the assets are not wasted in some way.
If the estate is larger or if there are complicated assets that none of you feel comfortable with dealing with (properties held in joint tenancy with non-family, annuities, etc.), it would probably be in everybody's best interests to hire an attorney. Although it may seem like a large amount of money, it is usually worth it so that everything gets done right. Also, it should be noted that the estate will pay the probate attorney fees.
Finally, one other thing to consider about hiring an attorney is that the attorney does not have emotional or familial connections to the estate. I have seen some really sad cases where families have been torn apart over probates. Attorneys can't always prevent that, but there's a better chance that it would devolve into squabbling if there's a third-party and neutral person that can make sure that everything is done according to law.
Here are a couple of other sites that have some good information about Illinois probate:http://www.probateillinois.com/http://illinois-attorney.com/probate.htm
Whoops, I seem to have written a novel! Hope this helps!