Never found out!
And even though we were all quite certain we saw parasite eggs on her fecal exam, the lab we sent it out to (because we weren't sure WHAT kind of eggs they were) said that her fecal was negative.
So she got treated for nothing and both dogs eventually became normal again, with no vomiting and normal stools.
Also - whatever that thing was, it ended up growing mold after a couple days. Which leads me to believe it was a THING and not just like, some weird inanimate object that she ate? I don't know! Super weird!