By Peter Gould BBC News Online correspondent in New York

For some families, the loss of a husband or father on 11 September was only the start of their nightmare.

One year on, they are living in fear of being deported.

They are the families of "undocumented" workers who died in the wreckage of the World Trade Center.

That is another way of saying they were illegal immigrants, who were not entitled to live and work in the United States.

They gave a false social security number to their employers, and hoped the authorities would not catch up with them.

It would be the coldest form of discrimination imaginable to carve the names of those undocumented victims on our 11 September monuments, yet leave their families at fear of being deported

Bill Granfield

But in death, their illegal status poses a problem for bereaved families trying to obtain financial support from government agencies.

Their cause is being championed by the Hotel Employees and Restaurant Employees International Union.

On the morning of 11 September, 43 of its members were working at the World Trade Center.

They had jobs as cooks, dishwashers, waiters and bartenders.

Obstacles

Fifteen of them were "undocumented".

They were trapped on the blazing upper floors, and were unable to escape. All died.

"They were breadwinners, the parents of young families," said Bill Granfield, president of the Local 100 branch of the union.

Bill Granfield - head of the union which represented workers

"The families suffered this terrible loss and then encountered a mind-boggling maze of obstacles trying to get the essential relief they needed."

Some families were afraid even to go into the union office to get assistance. To add to their problems, many spoke little English.

Carmen Mejia from Ecuador lost her husband Manuel. The union is now trying to ensure she can remain in the United States with her children.

"I was afraid to go for help because I have no papers," she told a union conference, speaking through an interpreter.

"My children and I are going to continue to fight for a future in America, because that was my husband's dream."

Long-term support

The union says other families have faced similar problems, and still worry about sent back to their own countries.

After the attack, when a loved one failed to return home, they were afraid to approach the police or hospitals.

Some charities have paid out without asking too many questions. But the problem has been how to get longer term support.

Union charters that date back to the 19th Century

Social security is supposed to provide a monthly payment for the surviving spouse until he or she remarries, and for the children until they are 21.

But the union says some families have been discriminated against, because they were not eligible for a range of benefits.

"For undocumented immigrants, their families couldn't collect social security, even though deductions were made from their pay, in some cases for years," said Bill Granfield.

But even the families of workers with legal status could face a lean time, according to their union.

The amount of compensation they receive will be based on the age of the victim, and a projection of their lost earnings.

The family of a highly-paid executive may receive between $1m and $2m. But the dependents of a catering worker can expect substantially less.

According to the union's estimates, the family of a typical restaurant worker might receive $600,000 - $800,000.

"If you've got a young family with kids to bring up, that sort of money is not sufficient," argues Bill Granfield.

Compassion

But the prospects for the families living and working illegally in New York may be worse.

The union wants an assurance from the government that the families of these "invisible victims" can remain in the United States, as an act of compassion.

"These people left their homelands to take a risk to come to the land of the free in pursuit of the American dream," said Bill Granfield.

"Now a part of their families, the ones that were lost, will never leave America, and their families want to stay here."

"It was their dream to bring up their children in America, and we think the government could offer them permanent legal status."

"It would be the coldest form of discrimination imaginable to carve the names of those undocumented victims on our 11 September monuments, yet leave their families at fear of being deported each minute they live in the United States."

Click here to watch residents of New York give their views about September 11