Former nurse Sheila Lovatt, from Ashley, near Market Drayton, was taken to hospital in May 2011 following a fall at home.
She had X-rays and a CT scan to look for damage to her shoulder but the X-rays were not formally reported on by a radiologist.
Following Mrs Lovatt's death the family wrote to the Royal Stoke University Hospital with concerns about other aspects of her care and treatment.
Her family have now successfully brought a legal claim against the University Hospital of North Midlands NHS Trust, which admitted that a series of communication errors contributed to Mrs Lovatt's death.
The case was settled out of court for an undisclosed sum.
In a statement, the family said: "The financial compensation is irrelevant – it has never been about money, we simply want people to know about the shocking care that my mother received from the NHS. There was failure in communication throughout – at all levels.
"To know that something as important as a cancer diagnosis can be lost in a fax machine is just staggering. We are absolutely heartbroken."
Miranda Hill, a clinical negligence solicitor at Lanyon Bowdler, said it was one of the worst instances of communication failure that she had seen.
"There were clear failings and numerous missed opportunities from the point that Mrs Lovatt entered the hospital following her fall until her sad death on April 3 2012," she said.
Liz Rix, chief nurse at University Hospitals of North Midlands NHS Trust, said: "The trust fell short of the standards it sets itself in diagnosing Mrs Lovatt's condition and has since put in place more robust processes to prevent this from happening again."
The CT scan was only reviewed by a radiologist in August of that year, despite guidelines at the trust responsible for Royal Stoke University Hospital stating images should be looked at within seven days.
In the meantime, the 65-year-old underwent surgery on her shoulder with doctors unaware she had lung cancer. When the scan was examined, the radiologist identified possible lung cancer and sent an urgent fax to the doctors caring for her.
The fax was never received and no system was in place for ensuring that incidental and unexpected findings on scans were investigated fully.
Mrs Lovatt was discharged from hospital after her shoulder surgery, but went back to her GP three months later after feeling progressively more unwell. She was admitted back to hospital when a neurosurgeon realised there had been a delay in picking up her cancer and asked for it to be investigated, but that never happened either.
Mrs Lovatt died on April 3, 2012, 11 months after first attending the Royal Stoke University Hospital, where she had previously worked herself as a nurse.
Her family say she was never made aware of the delay in diagnosis and treatment of her lung cancer, nor the fact the neurosurgeon had asked for an investigation into the standard of care that she had received.
Mrs Lovatt's family wrote to the hospital with concerns about other aspects of her care and treatment, following which the delay in her diagnosis and failure to investigate – despite the request of a senior neurosurgeon – came to light.