Showed up in the news today (well, a little before, but still). You need a Petpet equipped to do this, and apparently there's an NC item you can give to it as well?
Jelly Neo has a guide up.
So far, no one's pets have come back from adventuring yet, so who knows what happens when they do.
Your petpet does show up as this image on your lookup while in Grave Danger:

Also, you cannot unequip your petpet while it is in Grave Danger.
The status seems to change every hour or so (I'm on my third - so far something about Chewing on a cultists robe, Found a Peanut, and now Dug up some bones and played with them for a bit.)
I used one an extra Purple Valeous from the event drops that I still hadn't sold and equipped it to my labbie. In other words...if something happens to it, I'm OK with that...





