Upvote:4
There is no exit check on US borders, so the US can't stop you from exiting the country. You also don't need a passport for entry, just your Green Card.
However -
So, although you CAN exit and enter the US, there is nowhere much you could go.
Upvote:8
A passport is not required for green card holders to enter/exit the US, only a valid green card.
In fact, the US has no border control on exit.
So, if the other country accepts the expired passport, this trip is 100% fine.