The woman unzipped the small blue tent on a pavement on Skinner Street at lunchtime on Friday October 13 2017, the inquest at Wakefield Coroner’s Court heard.
The inquest was told the woman was concerned when the man inside failed to respond and she contacted emergency services.
Police attended and found 54-year-old Jeffrey John Hepburn’s body in the tent on Skinner Street, which connects to Wellington Street in Leeds city centre.
Mr Hepburn was pronounced dead just after 3pm that day.
Police Constable Deborah Box said Mr Hepburn’s death was treated as unexplained until an investigation found no suspicious circumstances.
Senior Coroner Kevin McLoughlin said a post mortem revealed Mr Hepburn died from a haemorrhage of blood from a cut to his right wrist, which had severed an artery.
Toxicology tests revealed evidence that Mr Hepburn, who had lived on the streets for many years and had drug and alcohol problems, had used cocaine.
The inquest heard Mr Hepburn regularly visited Mill Hill Unitarian Chapel in Leeds city centre and told minister Joe James he had been a sergeant in the army.
Recording an open verdict, Mr McLoughlin said there was no suicide note and he could not be certain Mr McLoughlin had intended to take his own life.
Mr McLoughlin said: “I pass on my condolences to his family.”