Thanks all for the suggestions. I didn't have the press cutting asking for anyone with claims on the estate to pipe up. Interesting. Thanks.
AMONDG suggests probate would have been in Canada if Joseph was living there. However, per his obituary he died while merely on a trip there to visit his father and for his health. His residence was Fulwood Rd Sheffield, as per the press cutting Comberton posted.
I'm going to look at the non-indexed probate records in Family Search Catalog suggested by MCKHA489. I am familiar with this rabbit hole and have spent many fruitless hours hunting through the millions of scans there, unearthing the occasional diamond.
I know quite a bit about the lives of Joseph's parents, Joseph Elias and his wife. They were Plymouth Brethren and lived in Oshawa for 30+ years. Joseph Elias died after his son (in 1914). Quite possibly his strict inward-looking religion would preclude him inheriting from non-Brethren. (I'm guessing).
Also, sister Martha was involved with the BHC (
https://canadianbritishhomechildren., .com) and accompanied several children to Canada, including Martha and Jessie Gott. Martha died 1917 in Canada.
I also know about Joseph's wife, Emily. They were living separately by 1891 Census. After Joseph died in 1904 she ended up in Eccleshall Bierlow Workhouse. In 1911 Census she is in Chesterfield workhouse. In 1913 there are press cuttings related to a court case after she tried to drown herself. Here is one quote
"Mrs Nodder, whose appearance and speech suggest that she has seen better days, was again brought before the Chesterfield Borough Bench to-day.
Chief Constable Kilpatrick said the woman, who formerly lived in Sheffield, had been in Chesterfield for five or six years, and during the early part of that period she had received an allowance from her husband, who had emigrated from Sheffield to America. Latterly, however, she had been thrown on her own resources and had earned a precarious livelihood by hawking. She had occasionally, when existence had become more than usually difficult, gone into the Workhouse, and the climax arrived on Friday, when she tried to drown herself in the River Hipper near to Clayton Street, Chesterfield. Her remark to him afterwards was that she "had not the courage to do it."Emily died 1915 in Chesterfield Workhouse. Clearly, therefore, she did not inherit Joseph's estate, even if she had good legal claim.
I shall keep hunting... Thanks again