With only days until her family's visa to live in Australia expires, mother-of-three Jessica Lee speaks emotionally of the links to her adopted country.

"I really just hope that the Minister changes his mind and just gives us a chance," she told SBS World News.

"We live in Australia. Just because... Australia is my home, you know? And I really want to give a chance for my sons to live here."

Ms Lee and the family arrived from South Korea in 2008.

Her husband, David Lee, proceeded to set up a series of businesses. But he says an unscrupulous migration agent he hired to get him permanent residency fled the country with more than $100,000 of his money.

"I am so very sad, and my family is facing a very difficult situation. And we just want the Minister to consider again our situation."

SBS World News

With poor advice from another agent recommended by the government on how to handle his company structure, subsequent residency bids failed.

A request for Immigration Minister Peter Dutton to intervene in the case was denied in May.

Now, the family can only appeal for him to change his mind.

Daniel Lee, one of two sons studying science at university, says it is not the family's fault.

"We are very frustrated, because we are actually facing deportation for something that was not done by us.

"It's not really our fault. We just trusted the agent and a registered lawyer, and we still don't know what we should do. And we just hope the minister could reconsider our case."

Bryan Lee, the other son studying science at university, says a return to South Korea would mean two years of compulsory military service and little chance of completing their degrees.

"Just the uncertainty is straining and stressful, because we don't know where we are going. It's just like walking in the darkness. It's just... yeah, it's pretty depressing."

Their 11-year-old brother, Richard, has known little but life in Australia.

SBS World News

During more than nine-and-a-half years in Australia, the Lees say, they have been active in many community groups, including the local Catholic parish in Melbourne's east.

The Syndal's Saint Christopher's Parish has set up a petition calling on the minister to let the family stay.

The online petition has attracted more than 4,000 signatures.

Father Patrick Jackson says the Lees are simply bewildered by their experience.

"They are a loyal, faithful, hardworking family. They've done nothing wrong, " says Father Jackson.

"They are the kind you want for Australia. They don't know which way to turn, because they've tried every avenue lawfully to try to get acceptance in Australia. It's almost like everything they've tried has been turned against them."

The Department of Immigration and Border Protection says the case has been assessed and those who have exhausted all avenues to remain in the country are expected to leave.