Certain crimes (aggravated felonies, crimes of moral turpitude) can make them deportable and cause loss of green card.

Even less serious crimes can delay or block naturalization, as they impact the “good moral character” requirement.

USCIS may place them in removal proceedings, where an immigration judge decides their fate.

In some cases, they may apply for relief (like cancellation of removal) depending on length of residence and family ties.