If an illegal alien violates immigration or criminal laws while in the United States, he or she may be deported or removed from the country. As removal is a formal legal process, the person being deported has the ability to challenge the deportation on a variety of different grounds.
The first step in a deportation is the issuance of a Notice to Appear by the United States Immigration and Customs Enforcement. This notice will contain the reason why the alien is a candidate for deportation. A hearing is then scheduled to determine whether the individual needs more time to find an attorney or will proceed without one. The NTA is then reviewed, and a determination is made as to whether the alien is going to be deported.
Once a decision has been made, the individual up for removal has the ability to file for relief from a deportation order. A hearing on the application for relief will then be scheduled. Another decision will then be made as to whether the alien is allowed to stay in the country or must be deported. An appeal to the Board of Immigration Appeals if a deportation ruling is held. Theoretically, it may be possible to appeal a case to the Supreme Court.
Those who are scheduled to be deported may wish to dispute the deportations with the help of immigration attorneys. While there is no requirement for the court to provide an attorney, it is possible to have legal representation during the deportation process. An attorney may be able to convince a judge residency issues can be cleared up or that any crime committed was a minor infraction. This may be enough to allow an individual to stay in the country.
Source: Findlaw, "Deportation", December 04, 2014