Sarah Jane probably had died by 1861 as not with family. There is no Bolton death, but a death at Radcliffe, in 1857 Bury of the correct age. Is is quite likely her, as there was no corresponding Bury birth in 1856 for another child.
Lancashire Death indexes for the years: 1857 MATHER Sarah Jane 1 Radcliffe, Bury RAD/7/24
MATHER, SARAH JANE 1 GRO Reference: 1857 S Quarter in BURY Volume 08C Page 267
General Notes
Sarah Jane Mather, mother LEE was born 1856 and the birth registered at Edgworth (the only Lancashire Sarah Jane born 1856 and another born Manchester Q3-1857)
By 1861 Sarah Jane was not with assumed parents Richard and Betsy. She died in 1857, aged 1, and the death was recorded at Radcliffe, Bury.
There are several other Sarah Jane Mathers: 1) "Sarah", Daughter of Henry Mather & Sarah Blackburn 2) Daughter of John & Catherine Mather of Stockport