In some cases, the risk of transferring cancer or infection is a calculated one, one that the patient and his or her doctor knows about going in. Using organs from less-than-ideal donors, known as extended criteria donors (ECDs), has become more common, said Dr. Fredric Gordon, Medical Director of Liver Transplantation at the Lahey Clinic Medical Center in Burlington, Massachusetts.
There just aren't enough organs available in the United States, so transplant programs are taking more risks [with ECDs] rather than let patients die on the list instead," he said.
There are 84,722 patients on the waiting list for a kidney transplant, according to the United Network for Organ Sharing, and more than 33,000 new patients are added each year. In 2009 alone, 4,540 patients died while waiting for a donor kidney.
If the donor is known to have had cancer or to have cancer at the time of death, this "raises a red flag," said United Network for Organ Sharing vice president Charles Alexander, but isn't necessarily a deal-breaker.
"Each type of cancer has its own associated risk," he said. "Certain brain cancers are thought safe for a donor to have, others not, it's a donor-specific determination."
But transparency is key in such situations. The risk needs to be something the patient and his or her doctor decide is worth taking, the Lahey Clinic's Gordon said.
Dr. Scott Johnson, surgical director of kidney transplants at Beth Israel Deaconess Medical Center in Boston, estimated that about 5 percent of donated organs nationwide fall into the high-risk category.
Although only 1 percent of transplant cases will actually result in a disease transmission, Wisconsin's Cronin noted, it doesn't make those rare cases any easier.
Liew's case was not the first of its kind for NYU Medical Center.
Two transplant patients received cancerous organs in 2008 after a donor from another hospital was mistakenly diagnosed with bacterial meningitis. The donor, who had actually died of lymphoma, passed on his cancer to three transplant patients, two of which later developed lymphoma and died.
The medical center tightened its requirements for proof of bacterial meningitis status in donors as a result of the case, but unforeseen transmission, as Cronin noted, is still possible.
At the same time, transplant surgeons say that it's essential to keep the donor pool as wide as reasonably possible because the risks rarely outweigh the slim chance of survival without a transplant.
"We should preserve the option of donation whenever possible," said Dr. Jeffrey Punch, chief of transplant surgery at the University of Michigan. "It's a tragic waste … to bury or burn organs that can save lives."
Gordon agreed, noting that while less-than-perfect donors carry extra risks, it should be up to the surgeon to know what's right and up to patients to decide how much risk they are willing to take on. "I wouldn't want a regulation stopping me from using an organ because it's not [100 percent] risk-free," he said.
The whole situation is tied up in different risks, Cronin said. "Once you go on dialysis, you're more likely to die than to get a transplant in the first place," he said. "Then you get into the risks of the organ itself.
"If I was to need a heart, liver, or kidney and you told me I had a 10 percent chance of getting a deadly disease, I'd say fine because without the transplant, my chances are even worse."
ABC News' Susan Donaldson James contributed on this report.