Have been looking for Back King St on 1911, but with a bit of comparison with the residents of that street listed on the electoral register in 1910, I've established it's called Austin St on the census.
Which leads to this family
https://www.familysearch.org/ark:/61903/1:1:X4M8-8W6
Mother appears to have maiden name Kershaw
The Census record listing the street name as being Austin St instead of Back King St., as stated on Louisa Stansfield's death certificate should be correct, perhaps it was just the local community at the time who knew it as Back King St. because Austin St. does run along the rear of the properties on King St.
Also, the family living at 17 Austin St. during the 1911 census was the Dawson family and there is a connection with Louisa Stansfield because Hannah Stansfield, Louisa's daughter born in Oswaldtwistle in 1885 married James Dawson the son of parents Margaret and the late John Dawson.
The 1911 census also records Louisa Stansfield described as a housekeeper living with James & Hannah Dawson's family at 4 Rimmington Row, Padiham.
So at the time of Louisa's death in June 1911 there's a good chance that someone from the Dawson family would have been with her when she passed away in the Haslingden Workhouse Infirmary.