It is likely he was in the Chester Union Workhouse on Hoole Lane. If you go to Google Streetview and the junction of Hoole Lane and Housesteads Drive you can see the former Chapel. The Workhouse graveyard was in the grassed area. Being paupers, nobody had a gravestone. In recognition of this, a commemorative gravestone was laid there. If you email me, I can send you a picture and an article about it. On Streetview you will see the curved brick wall and you can just make out the gravestone lain flat behind it. If he was in a different Workhouse, I am afraid I don't have any detail.