The drug conviction will make him deportable as well as inadmissible to the US if he travels. He should absolutely not travel to the US. You don't say how he entered the U.S. but if he entered lawfully and then overstayed a visa for purposes of cancellation of removal for certain permament residents his lawful entry would begin his 7 year clock for continuous residence. If the day he committed the crime was more than 7 years after his first lawful admission and his crime is for possession and not sale he appears to be prima facie eligible for Cancellation. You need a consultation with a qualified immigration attorney who can review the documents and give you a legal opinion. Waiting 5-10-20 years isn't going to make this conviction go away. You also need to understand that adjudication withheld is a conviction for immigration purposes.
Generally, except for one conviction of possession of 30 grams or less marijuana for personal use, any conviction involving controlled substances may be a basis for deportation. As the statutes are written, there is no time limit when the conviction may be used to deport the alien.
Thus, if your son's conviction makes him deportable, waiting 5 years or 20 years would not help him as long as the law remains as it is today.
He should review his facts with an attorney to see whether he is subject to deportation.
Since employers are supposed to check a person's citizenship or immigration status, your son may be unable to work if his potential employers do not accept his expired green card as proof of his authorization to work.
Incidentally, if you or your son's other legal parent is a US citizen, you can check if your son gained US citizenship through his parents. If he is a US citizen before the drug conviction, he likely cannot be legally deported.
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