I noticed a "New" Illinois Death Index database on the Illinois State Archives website. The New index is for Illinois Deaths from 1951 - 1971. They have already had the Pre 1916 Death Index and the 1916 - 1950 Death Index for all counties in the state. The 1951 - 1971 is flagged as "New", but I do not know when it came online. I just noticed it today.
It is a new ongoing indexing project, so not all records are reflected yet, so bookmark it and keep going back. I have found a few of relatives in it already, to either confirm, or find new information.
https://www.ilsos.gov/departments/archives/databases/idphdeathindex5171.html
It is part of an extensive list of database records on the Illinois State Archives website:
https://www.ilsos.gov/departments/archives/databases/home.html