I can't find anything about Mary after 1901 but I have found her baptism. All needs checking.
29th December 1875 in Burwardsley, daughter of James, a Shoemaker, and Mary.
I believe that the marriage of her parents was:-
James Jones, widower age 46, Shoemaker of Crewe, son of Samuel Jones, deceased,
Married Mary Price, spinster age 38, of Crewe, daughter of Charles Price, deceased
in Crewe on 9th July 1872
Witnesses: John Price and Margaret Ann Reeves.
I am not sure about their ancestry, but there was a Mary Price, daughter of Charles and Sarah, baptised in Burwardsley on 4th June 1835. However, she doesn't seem to be with them on the censuses.
I think this is James in 1861:-
Lower Town, Burwardsley
James Jones Head 38 1823 Shoemaker Halton, Flintshire, Wales
Lydia Jones Wife 34 1827 Shoemakers wife Willington, Flintshire, Wales
Martha Jones Daughter 8 1853 Scholar Burwardsley, Cheshire
James Jones Son 6 1855 Scholar Burwardsley, Cheshire
John Jones Son 4 1857 Scholar Burwardsley, Cheshire
And 1871 with different birth places:-
Fowlers Bench, Burwardsley
James Jones Head 50 1821 Shoemaker - Shropshire
Lydia Jones Wife 44 1827 - Shropshire
Martha Jones Daughter 18 1853 - Cheshire
James Jones Son 15 1856 - Cheshire
John Jones Son 13 1858 - Cheshire
Lydia was buried in Burwardlsey on 1st June 1871, age 46
James Jones, son of James, married Lydia Shone, daughter of Edward, on 26th December 1844 in Wrexham, Denbighshire.
David