First I did an Advanced Search for Annie's death certificate on FamilySearch. Her name, date and place of death, and name of the cemetery confirm this is "our" Annie:
Then I looked for the couple on Find A Grave. Margaret's entry includes a transcription of her obituary. She has a daughter named Catherine. No Illinois birth record match for Catherine on FamilySearch.
In the 1892 Chicago City Directory, John A Bacon, policeman resides on Portland Ave. And here's a possibility for the family in the 1900 census:
Catherine, Mary and Elizabeth still live with their parents in 1910:
But how do we know this family is Annie's family? If these were my ancestors, I would search for more documents with the address mentioned in Annie's obituary. I'd also like to see a reference to her in either parent's obituary.
Since this is a rudimentary search, I hypothesize that Annie's family moved often. While there are multiple addresses, the same group of family names appear together frequently enough to believe John and Margaret are Annie's parents. I added John's death to Find A Grave and linked Annie with her parents. If you know more about this family, I hope you'll add a comment below.
Note: I have no connection to this child. In A Child Lost ~ Introduction, I shared my hope of reuniting these children with their parents. If you are a Bacon descendant, I hope you'll give Annie a special place in your family tree.
My own genealogy work-in-progress is online at Living in the Past Lane.