This is completely conjectural speculation and may be totally off target.
To be admitted to Holsworthy Woorkhouse, Elizabeth Brock would have had to have been resident in one of the 23 parishes that made up the Union.
Assuming you have correctly identified her death in 1857 at the age of 29, this suggests a birth circa 1827-29.
I can find only one entry in 1851 that satisfies these criteria.
Betsy Brock, 22, born Bradford, unmarried, living in Bradford with her married sister. Also present are 2 lodgers. Is it possible that at a later date William Dawe took up residence as a lodger? I have not identified a person of that name living locally in 1851. Of course, there is the question why she was not able to have her child at home in the care of her sister.