May be absolutely nothing, but there is a baby in the Northwich Admissions book (which IS on FindMyPast) recorded as being born in the Workhouse 29 Sep 1882. She was discharged on 3 Nov, same date as a Martha Foster who was admitted 27 Sep 1882. Her name was given as Florey Foster, and on GRO Online, she appears to be illegitimate.
And I can't find her on the 1891 Census, nor can I see a death. Or a baptism.
Now, that may not be her, but if your Martha was born in the Workhouse, she would have been recorded as an admission at birth. Entries in the Admissions book are recorded under the first letter of the surname, and then by date of admission. It could be a bit of a trawl, but could turn up possibles.