The green card should always be at hand
Yeah, he can't do that. He needs a green card in his possession anytime he's not on private property. Obviously for instance leaving it in the gym locker while you're at the gym is ok, but no, you can't dash off to the grocery store without it, on the logic that it's "just in town". Just like I can't make a milk run without my driver's license. So this idea of dashing off on a 400 mile adventure, is Right Out.
He should have absolutely refused to travel without the documents in hand. If they say "get off the property or we'll call the cops", then tell the cops "I can't leave without my passport/green card" which the cops will back up, because they know the law and they know how trafficking works.
The right to strut around the USA without any ID at all is reserved for US citizens only, and even that is being stripped away by ever-changing laws.
Those documents are someone else's property
The Green Card is the property of the USA and is not hers to steal. The passport is the property of the Philippine government and is not hers to steal. She didn't take your stuff, she took theirs. So she is guilty of a Federal crime, and the long arm of Philippine law may have an "opinion" on the matter also.
Of course, most people don't think of it that way. They think your ID is your property so they think they're only messing with you.
I would absolutely, positively report theft of the passport to the Philippine consulate. (Or rather, just report a missing passport, and be free about explaining the circumstances). One might hope that a phone call to consular staff might scare her straight, and get her to send it along. Most likely the green card would be in there also. Or, he could pay the fees to have a replacement passport issued.
However the important one is the Green Card, since that establishes your right to be in the USA. On that one, you must consult an immigration lawyer and find out what you need to do. You certainly can get replacement green cards (not cheap), but admitting you don't have yours could cause you problems.
People often seize documents for a reason
And what makes me think that is, the uncle is a grown adult and the daughter's elder, and I thought that meant something in the Philippines. He is supposed to be more adult and more responsible. As such, he should be responsible for his own documents. Yet, this seems to be in the daughter's hands; this raises red flags.
Maybe what she did was a harmless prank. But usually, taking an immigrant's documents is done for an entirely evil reason. Either they are forcing them into indentured servitude (also called "trafficking") - so if he is now in a situation where he is being extorted to do work in a worse situation or worse wage than he'd take willingly, then he is a trafficking victim, and the taking documents is part of the plot. The US has some legal protections for trafficking victims.
Or they are "setting him up" for failure in some other way - for instance, out of idle malice, the niece might be planning to call immigration and report him as being illegal, hoping he'd be found with no green card, and deported for not having it.