If an illegal alien is detained by Immigration and Customs Enforcement (ICE) or has received a Notice to Appear in Immigration Court, they have the right to ask the Immigration Judge if they can be permitted to remain in the United States in order to apply for permanent residence.
In order to qualify, the alien must prove that they have been present in the United States for the past 10 years and have either a spouse, parent or child who is either a lawful permanent resident or a United States citizen.
The immigrant must also prove that the U.S. citizen family member would suffer exceptional and extremely unusual hardship were they to be deported. An illegal immigrant with a spouse, parent or child who has a very serious or acute medical condition that cannot be treated in their home country may be able to prove exceptional or extremely unusual hardship to that person.
This would also be the case for an illegal immigrant who has children, over the age of 12 who are U.S. citizens. The immigrant must prove that the child would face exceptional and extremely unusual hardship should their parent deported.