Find a Lawyer
The process of legally removing a person from the U.S. is known as "deportation" or "removal." In order to be removed, grounds for deportation must be proven to exist to an immigration court. The burden of proof is on the government.
There are many grounds for deportation, including any fraud or misrepresentation while applying for a visa, or even citizenship. Even if a person has become a naturalized citizen of the U.S., they can lose their citizenship and be deported if the government finds out that they misrepresented a material fact at any stage of the process, from initial entry all the way up to naturalization.
Furthermore, an immigrant can be deported if they commit a serious crime, such as murder, rape, drug trafficking, or gun running. Less serious crimes can also be grounds for deportation if they involve "moral turpitude."
These are crimes which may not have the extreme negative consequences of the ones mentioned above, but which clearly demonstrate that the person who committed them is of poor moral character. They include things like fraud, embezzlement, and theft.
A person can also be removed if they overstay their visa.
Restrictions on Deportation
There are many reasons why the government might be unable to deport someone, even if they are not technically in the country legally.
One of the big ones is amnesty. A person can apply for amnesty virtually any time (as long as it's within a year of their most recent entry), and if the government finds that the grounds for amnesty exist, they cannot be deported, at least for the time being.
A person can also apply for voluntary departure if they're facing deportation. This allows them to voluntarily leave the country, without having actually been deported. This means that if they want to re-enter the country, and apply for entry through the proper legal channels, they don't have a prior deportation on their record, making the process much easier.
People who are being deported because they've been convicted of serious crimes usually don't have any of these exceptions available to them. However, they are, at least in theory, covered by the Convention Against Torture (CAT). The CAT is an international treaty which the U.S. has signed. All signatory nations agree that they will not deport anyone (regardless of who they are or what they've done) to a country where they are likely to be tortured. The U.S. is generally pretty good about honoring its obligations under this treaty, when it can be proven that a person will be tortured in their home country.