I'm just catching up on family research after a while away from it and my eye was caught by this thread.
There are some matters here that seem to link into my family. My Gt. Aunt Polly (Mary) Shortall (née Coyle) lived with her husband, (latterly Sir) Patrick Coyle in 47 Hardwicke Street, and as far as I knew, the house was given them by her father, Patrick Coyle as a wedding present. If true, a handsome present! That, at least, is the story handed down.) My paternal grandmother, Elizabeth Ann Monks, Polly's sister, lived in No. 46. It was she who told me that Polly had lived next door. There was never any indication that Shortalls did not own the house. Quite the contrary.
Polly died in 1915 while the family were still living at No. 47; and Sir Patrick in 1925, but by then he seems to have moved to Clontarf.
The Monks family also had property in Buckingham Street, Nos 3 & 4. My Gt. uncle Nicholas Monks was left a share in the properties in my Gt Gt grandfathers will of 1902. The odd thing is that he (gt. uncle) died in 1928, but in No.37.
Desmond, if your forebears lived in No. 47 Hardwicke Street and 4 Buckingham Street it raises an interesting situation. My personal recollection of Hardwicke Street is of horrible tenements that had permanently open doors, no lighting of common areas, poor sewage. Clearly it was not always like that, and No. 46 at the Frederick street end was always single family house. And from personal recollection, No. 47, unlike other most other houses in the street, always had a locked halldoor. I assumed on this basis that it too was a family house. I should perhaps add that I can recall Hardwicke Street going back into the late 1940s when air raid shelters occupied the centre of the roadway.
I am at a loss to explain how Shortalls and your family lived in the same house. Shortall, who was some kind of builder, was far from being a poor man. But this does not fit with the fact that they lived there even after Shortall would have moved out. Perhaps one or the other family owned the house and leased a floor, as Shane has touched upon.
LATER
I have looked at the 1901 and 1911 Censuses and I find I have to revise, yet again, information that was passed down through the family as misleading or plain wrong. Yes, the Shortalls did live in 47, who the house belonged to I cannot say for certain. Certainly there were others living there, although on what basis they or the Shortalls shared the house, I cannot say at this stage - another fact to be established. Shortall is describer as a Builder, and at this stage he had not yet got his knighthood.
The connection of Buckingham Street AND Hardwicke Street with both our families is curious. This posting doesn't really throw any light on your original question, but it does suggest at some kind of link.
I have a picture of 47 Hardwicke Street of which I can let you have a copy, if you wish The houses (46 & 47) were double-fronted, but were only one room front to back. They had basement kitchens and outside were the areas overlooked directly by the footpath. The areas, at street level had protective iron railings set into granite kerbs. Three granite steps supported by an arch over the area, leading to the front door. Just outside the frontdoor there were shoe scrapers. There were cellars that extended out under the footpath, and perhaps partly under the road too. In my recollection those at 46 were used to store coal, which was delivered to the cellar through a manhole cover on the footpath. They had two storeys above the ground floor. No. 46, alas, no longer exists. Dublin Corporation acquired most of the houses in the street for housing development in flats. No. 46 was the last one they acquired. It broke my grandmother's heart as she had lived there since she had married in 1901.