Hello Gemma
I lived on Nechells Park Road until 1971 and I knew the "almhouses" well because my aunt lived there until she died in 1967. The building is marked as "James Almshouses" on an Ordnance Survey map of 1902 and they are still run by the James Charities - the place is now called called the James Memorial Homes - although the original buildings have all now been demolished and rebuilt. I don't know anything about the time when your relative would have been liiving there, but I suppose the James Charities might be able to give you some information.
When my aunt lived there all the residents were single women and there was a matron in charged of the place who looked after the residents' welfare and presumably was in charge of the administration as well. I don't recall if my aunt paid any kind of rent or not. Basically the Homes were a kind of sheltered accommodation as we would say now, a place where the residents could lead independent lives with a degree of security. So the term "inmate" just meant a resident and didn't imply any kind of coercion or control! In fact, my aunt, who never married, had a job as a secretary at a firm in the Kings Hall Market near the Old Square. I think she was happy living in the almshouses and I often used to visit her there. One day when I was visiting her I went to play in the grounds and the matron saw me. She got hold of me and smacked my backside, thinking I was a local lad messing about on her property!
All the best
Libermann