“Depending on the numbers of cancers and the criteria for those cancers, we would certainly be getting more and different claims than we were receiving previously,” said Sheila Birnbaum, the special master overseeing the Sept. 11 Victim Compensation Fund. “We cannot add any more money to the fund, so we would have to prorate what we’re giving to people depending on the amount of people that apply, the seriousness of their injuries, the economic loss that they’ve sustained.”

The advisory committee found some evidence linking Sept. 11 to increased rates of cancer, but existing studies are far from conclusive. And since there is probably no way to distinguish those who developed cancer from ground zero from those who might have developed it anyway, anyone who can prove sustained exposure could potentially be eligible for payment.

“There’s tens of thousands of people that are potentially eligible, so how do you sort through that?” said Dr. James Melius, administrator of the New York State Laborers’ Health and Safety Trust Fund, who has closely monitored the research. “Will it be everybody with lung cancer in Lower Manhattan who was there around Sept. 11?”

And many cancers may develop long after the fund expires in 2016. “You know they’re going to continue for 10, 20, 30, 40 years, and you have a victim compensation fund that runs out of money and that ends in about five years,” Dr. Melius said.

After heavy lobbying by the Bloomberg administration, Congress in 2010 approved the James Zadroga 9/11 Health and Compensation Act, named after a police officer who died years after working at ground zero. It allocated $2.8 billion for compensation for those sickened by World Trade Center dust, smoke and fumes, or their survivors. It also set aside $1.5 billion for treatment and monitoring.