That is (was) the collar of my Sybil sweater. The one I worked for ages on. The one that I love for its warm coziness on cool mornings. The one that my dog decided was oh-so-delicious.
Believe it or not, I do feel sorry for my little Lucy. She really only chews when she's stressed, and I'm not completely sure what's bothering her. (Fortunately, the yarn came back up, so she doesn't have a blockage. Unfortunately, I had to clean that up.)
Looking at this in a glass-half-full kind of way, it is lucky that Lucy only chewed one side of a sewn-on collar. She very kindly did not eat the center back of the sweater. So, Sybil goes to the mending basket, where I will detach the collar, and pull it back to the first un-chewed row, re-knit and re-attach the collar. After a good wash, it should be good as new.