If a green card holder or LPR who has a criminal conviction on their record leaves the US and returns, the State Department has the ability to treat them as an arriving alien. This gives immigration authorities much more leeway in deporting someone.
Many of the protections you have as a green card holder are lost if you travel abroad. This is part of the immigration reform bill passed in 1996 by Bill Clinton that strips back many of the protections for green card holders with criminal convictions.

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