The man died through blood loss when a venous port became disconnected, according to the report to Shrewsbury and Telford Hospital NHS Trust's board.
It has led to the Health and Safety Executive getting involved and an investigation is now under way.
The report says the man had a cardiac arrest in June and he later required dialysis.
It continues: "Whilst on the renal unit, by some means yet to be determined, the venous port became disconnected and the patient exsanguinated.
"This is a high profile case involving the Health and Safety Executive and Medicines and Healthcare products Regulations Agency and all relevant parties have been provided with relevant information.
"The investigation is progressing."
It was one of five serious incidents reported by the trust, which runs Royal Shrewsbury Hospital and Telford's Princess Royal Hospital, in October.
Other serious incidents involved a patient suffering a fall and another who died after being diagnosed with C.diff, although the report says her death 'was thought unpreventable'.
Another involved a patient being given a blood thinning medication which she should not have had, although the report says it is unclear what impact it had on her condition.
The fifth incident related to a delayed diagnosis.
It happened when a patient attended one of the trust's emergency departments with central chest tightness and shortness of breath.
The report says the patient was given an electrocardiogram and blood tests and she was triaged as a 'very urgent' case.
As the major cubicles were full, and the patient was still pain free, it was decided she could be temporarily placed in the ‘fit to sit’ area until a cubicle could be provided.
But according to the report, the department was so busy that patients in the waiting room were told the waiting time to be seen was expected to be seven hours, and those people who felt they could be seen by their GP or return in the morning were advised to do so.
It says: "At 10.35pm the patient was booked out of the department in retrospect. The time of departure was noted as 8pm.
"Her troponin result was available at 9.30pm. It was raised at 23ng/L.
"There was no review of the patient’s bloods after she left the department and she was not called back.
"We have been informed by the patient’s son that his mother felt she was adding to the burden of the department.
"She returned home but continued to have chest pain and the following day an ambulance was called.
"As the paramedic arrived, the patient went into cardiac arrest and was successfully resuscitated.
"She was taken to the tertiary centre and had stents inserted. She is currently recovering."
The report is expected to be discussed at a trust board meeting at PRH this afternoon.