If you look at the website Stroud Workhouse.
Records
Gloucestershire Archives, Clarence Row, Alvin Street, Gloucester GL1 3DW
Very few local records survive. Holdings include Guardians' minute books (1836-1930)
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There is an article on Gloucester Archives - Headed, Boards of Guardians and Workhouse Records
Type of record : Minutes of the Board of Guardians and its various subcommittees.
What will it include: Vary in the amount of details included. Can provie information about individual inmates especially if an extra cost to the Guardians was involved e.g. pursuing a parent who'd abandoned their family, etc. etc.
Registers of indoor relief or admissions and discharge register: Include personal details of individual inmates of the Workhouse. Vary in the amount of information given.
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Ancestry just has London, England Workhouse Admissions and Discharge Records 1764-1930.
Also
England and Wales, Long-Term Workhouse Inmates 1861 - which does include 20 people listed in Stroud. Giving the years and months how long they have been there - some for 20 years down to 5 years.