Cancellation of removal: This method can help prevent the removal from being completed. There are 3 routes for this to be accomplished. If the individual can prove they were in the US for the 10 years preceding the trial, 10 years of good moral character, or if there is an immediate family member who is a legal resident that will suffer a hardship.
VAWA and TPS: The Violence Against Women Act can help protect women who have suffered from domestic violence. TPS or temporary protected status can be granted to people who can prove their life will be at risk if they return to their home country. For more serious cases asylum can be granted to those who have suffered or will suffer persecution in their own country if returned.
DACA: Deferred Action for Childhood Arrivals can protect children who were brought to the US at a very young age and attended school without leaving the country.
I-601A: Filing for an I-601A can protect those who are married to a US Citizen or if their parents are US citizens.
I-751: If the individual is a conditional permanent resident and did not properly renew their papers, this can be petitions and renewed to allow for a new filing. Never file these documents on your own. Only a licensed removal defense immigration attorney should deal with these sort of things. Your future status as an American is on the line and no risks should ever be taken, especially with the I-751.
Adjustment of status: If the individual can file for a change in status from one entry permit to another, or awaiting confirmation for a permanent residency they can be protected before a judge.
Ensuring that you have the proper representation is so important because many times you only have one chance. The options listed above plus other more specific defenses can be difficult to determine which one can apply to a specific case and when and how to file the defense. Additional court and removal fees are expensive which makes it more difficult to file a second time. Having a well-trained and experienced attorney to counsel and represent you not only simplify the procedures but greatly increase your chances of succeeding.