Staff at Newgate Residential, on Newgate Street, left a note on the door on Tuesday, February 18 stating they were in a meeting for the afternoon and provided contact details if anyone needed to contact them urgently.
They also covered the window in big sheets of paper preventing people from looking inside.
However, since then the premises have remained closed, the phone line is dead, the website is now unavailable and the building stands completely empty.
Customer John Scanlan, of Eldon, is concerned about what has happened as his tenancy agreement means he is required to pay his rent in person at Newgate Residential every fortnight.
He said he has the money to pay but without details of his landlord he said he can only keep it safe until he discovers what is going on. So far he has missed one payment, but another is due shortly.
“I want to get in touch with my landlord but all I know is that he is from Glasgow,” said Mr Scanlan. “He might have tried to do the same but I just don’t know.
“We have the money but just don’t know what to do. They never said anything last time I went in to pay. I actually thought they had covered the window because they were decorating at first.”
He added: “We want to make this place our home. We have no plans to move but we have a problem with damp in the bedroom which we really need to get sorted.
“I am sure the landlord would help us but we haven’t been able to tell him. We have had to move the wardrobe about 18ins from the wall and I could scrape a layer of mess of the wall it is that bad.”
The Northern Echo has been unable to contact the owners of Newgate Residential for comment.
• Have you been affected? Call reporter Dani Walker on 01388-602232.