It’s legally called amnesty, which is a pardon applied to a whole class of people. It has been used a number of times in American history (especially after the Civil War). Individuals don’t need to be individually named or charged.
Doesn’t matter, as pardon/amnesty is only for crimes during a specified time and does not apply to the day after the pardon/amnesty specifies. An illegal entrant into the US could be deported as usual the day after the pardon.
The only hypothetical advantage MIGHT be that such a person could not be barred from entering the US in the future on the basis of past illegal entry, assuming they could get out of the US without it being officially noticed.
“It has been used a number of times in American history (especially after the Civil War). Individuals don’t need to be individually named or charged.”
In fact, amnesty and pardon to Confederate soldiers after the Civil War required that many had to make personal and individual requests for amnesty. They also needed to swear fealty to the United States and explain their actions before the war commenced and their actions during the war.
Amnesty Under Johnson
wnc.omeka.chass.ncsu.edu/exhibits/show/confederateamnesty/amnestyjohnson