There does not appear to be a lot of information about the Poorhouse available but Edward Chitham (in his 1972 book The Black Country) says
"The Rowley Poorhouse was situated at Tipperty Green where nowadays the Christadelphian church stands. It was a stone building, limewashed white and contained separate accommodation for men and women. In addition to stone breaking both sexes worked in the adjoining nailshop, which was closed in 1829 to provide space for a small sickbay. In the sickbay the floor was to be laid with bricks and the window looking out on to the garden stopped up, being replaced by another looking onto what is now the Dudley Road. This was to be "above the height of persons" who might look in and see the paupers."
Unfortunately he does not give his sources for this information but it tallies with what I have read elsewhere. Mr Chitham taught me Latin at Rowley Regis Grammar School in the 1960s and ignited my interest in family and local history then. He was certainly still alive at the time of the last school reunion in 2019 so I suppose it might be possible to ask him where he got this information.
A book called "Rowley Regis" by J Wilson-Jones (Librarian, Rowley Regis for many years), published in 1950 and which appears to be based partly on local records to which he had access and partly to conversations with local elderly people refers to Vestry records in 1820 (Probably now with Sandwell Archives) which required inmates to be employed breaking a certain quantity of stones before they were given a meal.
The rowleyvillage.webs.com website states:
"1738 Poor House – by indenture date 03/08/1738 in consideration of £50 Thomas Haden and John Turton had purchased of the Rev Thomas Saunders two dwelling houses or tenements situate at a place called Iberwick (later Tipperty) Green in the Parish of Rowley and reciting that the said messuages had been converted into a workhouse for the poor of the said parish. "
"1836 Rowley regis poor-house amalgamated with Dudley Poor Law Union. Rowley Regis poor house which was located in Treacle Street between Cock Green and the Knowle closed. Treacle Street no longer exists but its whereabouts can be defined from the 1861 census. Another site for an earlier or later poorhouse is thought to be at the junction of Tipperty Green by the Bulls Head."
Again, no sources are given!
Finally, my 4xg-grandfather is shown living in Tipperty Green in two censuses, along with an Elizabeth Thompson in each, in the 1841 census they are shown as of independent means (she as the Head of the household) but in the 1851, by which time my 4xg-grandfather was 88, both are described as Almspeople and he as a pauper. So some provision for the elderly poor continued in Tipperty Green as late as 1851, despite the amalgamation with the Dudley Poor Law Union. He died in 1852 so I have no later information.
Sorry this is all so vague but it may be of interest.