Experts say the odds of getting cancer from any single organ transplant could be as small as one in 10,000.
And they believe this is the first time one patient has passed cancer on to four recipients, and it has never been seen to take so long for tumours to develop.
Research by scientists at University of Tübingen in Germany and the VU University Medical Center in the Amsterdam, the Netherlands, revealed the strange tragedy which unfolded during six years after the donor died.
The experts insist donor screenings do work well enough and say there is a 0.01 to 0.05 per cent chance of getting cancer from any donated organ.
The first person to be diagnosed in the peculiar case was a 42-year-old woman who received both the donor's lungs.
Less than a year-and-a-half after receiving her new lungs, the woman was admitted to hospital because they weren't working properly.
Doctors then discovered she had breast cancer which had started in her lungs and spread to her bones – it later spread to her liver and she died in August 2009.
The disease is still called breast cancer even when elsewhere in the body because the tumours are made of cells specific to the original cancer which started in breast tissue but have spread.
Medics proved the cancer had originated in the organ donor by doing DNA testing.
When news got out about the lung transplant recipient dying, the 62-year-old woman who recieved the left kidney and the 32-year-old man who received the right kidney were both warned about the risk of cancer.
Tests were done on both but no sign of the disease was found right away.
But in 2011 the man was diagnosed with cancer in his kidney, and the woman was found to have cancer in her liver, but not until five years later.
The man had his transplanted kidney removed and took chemotherapy drugs for a year, and has been cancer free since 2012.
However, the woman's cancer, which was first noticed in her liver, then appeared in her kidney, bones, spleen and other organs in the digestive tract.
Her treatment was withdrawn and she died two months after being diagnosed – a full six years after first receiving the donor kidney.
The fourth patient to get cancer from the transplanted organs was a 59-year-old woman who recieved the liver, to replace hers which was damaged by cirrhosis.
Her tumour was detected in 2011 but she refused to have the liver removed, fearing similar complications to the ones she experience after the first op in 2007.
Researchers said 'she felt well' and treatment managed to stabilise the disease. But when the cancer began to spread in 2014, she refused any further treatment and died.
The scientists suggest keeping the organs warm without a blood supply could have allowed tumour cells which were moving in the bloodstream to settle in the organs and begin to spread.
And because the patients were taking drugs to weaken their immune systems to stop their bodies rejecting the organs, the cancer could have been able to grow unchecked.
But, they said, scanning donors too intensively could bring up minor problems leading to more desperately-needed donors being rejected.
The authors, led by Yvette Matser, wrote: 'The drawback of a routine postmortem CT scan for all donors is that it will increase clinically irrelevant findings, which might lead to more rejection of donors and a decrease of the already scarce donor pool.
'The extremely low rate of transmission of malignancies during transplantation proves the efficiency of the current guidelines.
'A complete medical examination, including a breast examination, should always be performed as described in the guidelines of the Organ Procurement and Transplantation Network.'
They added: 'This extraordinary case points out the often fatal consequences of donor-derived breast cancer and suggests that removal of the donor organ and restoration of immunity can induce complete remission.'
The findings were published in the American Journal of Transplantation.
