After reviewing the cards on H.J. Williams in Hilliard's Legion and the 59th I would bet he died at Camp Douglas, he was carried as AWOL in both Hilliard's and the 59th from the time of the battle of Chikamunga, Sep 20,1863 until Jan-Feb 1865 company muster roll when he was shown as KIA at Chickamunga.There are POW cards showing him captured on Sep 20,1863 then forwarded to Louisville Military Prison then to Camp Douglas showing him as a prisoner and as dieing Nov 1 ,1863.
Just my bet!
Mike