I don't know the answer, Cynthia, but I wouldn't give up on it. I tend to be an optimist. I'm not sure I'd trust my thoughts as much as most of the others here, but I can tell you what I would do because I've seen that before. I remember accidentally stepping over a bigger single scape, and breaking it so it looked like that on top. Where what's left of the leaves looks like concentric circles.
It's source of energy seems to be almost a total loss, but there is a little bit of green leaf still attached. If it were mine, I'd leave it on just in case it can get some energy from it. It looks worthless, but you have nothing to lose until you see it turning yellow or brown in my opinion. And I'd keep it well watered so it doesn't have to stress any more than it is.
If you're lucky, you will see the middle leaves start getting longer in a few days. I didn't want to say this, but I lost the one I broke off like that. But it's hard to tell what kind of damage happened to the crown in the attack. I would make it as comfortable as possible and see what it looks like in two weeks. When the last attachment turns yellow, that's when I'd remove that, but I'm thinking if it is going to recover, you might see growth from where the leaves came out before that happens.
Do you think the daylily will survive this attack? I've seen a groundhog in the area, so is this critter the likely culprit to chew off the leaf down to the crown and then discard the leaf? If yes, what suggestions do you have for deterring their habits? I'm not a good shot, so that suggestion is out. 
