Do you already have your Green Card? Unfortunately, if you have committed many types of crimes, you can be put into Removal Proceedings and deported. having the Green Card does not mean that you can stay here permanently and that you are safe from never being deported. Once you commit a crime of many different kinds, you could easily find yourself being transferred to immigration detention after you serve your criminal sentence. In that case, you would have to fight your case to stay in the U.S.

Application for Cancellation of Removal and Adjustment of Status for Certain Non-Permanent Residents 42(B). A Legal Permanent Resident can apply for cancellation of removal if they have maintained a continuous physical presence in the U.S. for 10 years, maintained a good moral character, and have not been convicted of an offense. The removal would result in exceptional and extremely unusual hardship to your U.S. or Legal Permanent Resident spouse, parent or child.

If that is the case, you could apply in many times for Cancellation of Removal. This is like a 'get out of jail' free card. It can happen once and if you win, you will get to keep your Green Card and stay in the U.S. even though you have committed a crime making you deportable.