Hi Charlie
From doing my research I have come across this before. The Cosy was indeed a common lodging house. It was based at 18 Pump Road, Oldham Road, Manchester. From what I know about common lodging houses is that they are like your modern day 'hostels'. At that time is was cheap accommodation along with poor standards. They could have ended up there for many reasons; maybe just passing through the City or struggling to find somewhere to live.