Elaine
It seems I was mistaken about your grandfather being in police custody in 1927. That person was definitely a different Harry Stagg who was 10 years older than your grandfather and was also living in Ecclesall Bierlow in 1921 census (Lime Street).
There is no doubt about your grandmother Annie Stagg. From our burials records:
Stagg, Annie (Widow, age 53).
Died at Winter St Hospital; Buried on November 22, 1938 in General Portion ground;
Grave Number 15465, Section OO of City Road Cemetery, Sheffield.
STAGG, Malcolm Stuart (Son of , age 1 mth).
Died at City General Hospital; Buried on July 21, 1942 in General Portion ground;
Grave Number 15465, Section OO of City Road Cemetery, Sheffield.
The child in the same grave is her grandson, son of Stuart born 1919
Here are 4 of Cyril's siblings from our Baptism records:
STAGG, Margaret (of 72 Harold St, born 1907-04-08).
Baptised April 24, 1907, by C C Ellis at St Bartholomew, Langsett Rd.
Parents name(s) are Annie & Harry Charles Stewart (Bootmaker).
STAGG, Edward Johnson (of 29 Tennyson Rd, born 1909-01-01).
Baptised January 20, 1909, by ~ at St Mary, Walkley.
Parents name(s) are Annie & Harry Charles Stewart (Shoemaker).
STAGG, Arthur (of 1ct 9h St Stephens Rd, born 1910-12-23).
Baptised January 11, 1911, by George Dart at St Stephen, Netherthorpe.
Parents name(s) are Annie & Harry Charles Stuart (Boot Repairer).
STAGG, Elsie (of 12ct 1h Young St, born 1913-12-22).
Baptised January 7, 1914, by A G Jones Curate at St Silas, Gilcar.
Parents name(s) are Annie & Harry Charles Stuart (Labourer).
I cannot find a death for Your grandfather Harry Charles Stuart Stagg b 1885.
"Harry Charles Stuart Stagg (died 1933)". I can't find a record in the deaths indexes either. A quick sampling of the family trees provides no supporting source of their information.
Elaine,
See Sheffield Daily Telegraph Saturday March 3 1928
Annie Stagg of 9 Cundy St. was bound over for 12 months for wilfully abandoning her 6 children. Her husband had abandoned her 3 years before and all efforts to trace him had failed.
She and her children had from time to time been under the care of the Guardians, who were reluctant to relieve the children unless the mother also went into the workhouse.
There are many more details.
See also Sheffield Evening Telegraph 5th March 1920,
Annie Stagg of 12ct 1 H Young St was fined 5s for not sending her children to school.