After getting this encounter I went back to the Tunnels and tried to get another jade amulet, but no go. When I got to the Towering Figure I did not see any new options there. I ran away so I could keep working on this. I have not yet bumped into the faceless hunter again in the book, and I spent some time wandering around while Etheric in Southside Park seeing if it had gotten out into the real world, with no luck.
On one hand, the Faceless Hunter encounter seems to lead you to The Black Book zone, so maybe this is one more step on the road to whatever the amulet can get you. On the other hand, I worry that the amulet and the hunter are gone forever and I was supposed to do something with the amulet before it got ganked. Like, maybe you have to fight it in the real world to keep it from taking the amulet? I'll keep looking, but I'm worried that I missed my chance at whatever-it-is this run. :/
EDIT: I also forgot to check whether the jade amulet actually shows up in your real inventory when you get it. Probably not, but it's probably worth looking.