Wow, they had a feast, huh? I did some research today, and asked around ... found out that Cankerworm might be the culprit. I've been lucky in never having had to deal with them. There are specific sprays for them, but I have no experience with that. I wouldn't shear them this summer, just let them recover. Yours is pretty thinned out, so I can't predict what will happen, but they're normally pretty tough plants. Also, I see a few dark brown leaves in there, and can't tell if that's related, or something else is going on. I don't know where you're located, your growing conditions, etc. You might want to take these pics and a cutting (both eaten and brown parts) to a trusted local nursery and see what they think.

If it's evergreen, then possibly Dahoon. Leaves are really chewed up, so hard to tell. Dahoon has mostly entire margins (rather than spined). It is a US native. But I don't think I've ever seen Dahoon with scalloped leaf margins? Maybe there's some variability?

When I got my land, the first thing I did was start thinning out the brush so I could walk around.. I had to thin just to see the lay of the land and where I wanted too put the house and workshop. It was THICK! I had a impenetrably thick regrowth cedar brake that's killing off my red oaks, madrone and live oaks I started going around to county extension meetings and other seminars. learning about the land around me and all the different philosophies about land restoration. I have learned to do more with less labor and lowered my expectations to fit the land. I have learned how to do more harnessing of the natural process and letting the land be itself.

You might have gotten more response if you had copied the photos and all here to this forum. It's also been less than 24 hours and most folks have other obligations that may slow responses. Typically holly wood is quite white from everything I've seen. There aren't photos of the branch before removal, so it is difficult to diagnose what the problem was that caused the leaking sap. The dark wet spot looks to be a former injury that is healing over (see how the edges are rounded and look to be growing toward the center of the hole?) but trapping water. I am also not sure if the photos of the cut branch are of what is still on the tree or the part trimmed off. If it is still on the tree, it looks like the remaining stub is a bit long. Read up on proper pruning so that you are down near the branch collar but not cutting into the branch collar since that will create the best environment for healing. I can't grow holly here since we are so cold so don't have direct experience with this plant. I would be patient. Either it will heal or it will continue to decline, and time will answer that. There is not anything you can do to make healing happen faster. If you are concerned and there is space to plant a small replacement nearby, you could do that. If you add photos of the cut part that is left on the plant and the plant as a whole, not just the bark part of the branches, you may get some additional input on how healthy the remaining plant is.