Thank you!
Of course, I hope you understand if my first instinct is not to assume that my late father and grandmother lied to me.
None of us was there when the baby was delivered. The baby did receive a name, and has a death certificate, one day later. Is that how stillbirths, or abortions for that matter, are normally recorded? The death certificate says that the cause of death was premature pulmonary atelectasis. No other medical information.
My grandmother's story about her husband's death was that he was spying on the union for his corporate bosses, and caught a case of "lead poisoning". Not hard to believe in Chicagoland of the '30s. There would still have to be a death record of some sort, unless the body was not recovered.
My grandmother remarried and moved to Arizona. One can imagine she would be reluctant to talk about her first husband while her second husband was around, and certainly forget about where he was buried. Anyway, she is long gone, as is my father.
Anyway, I will go ahead and search Illinois more broadly. Thanks!