All You Do Is Cry

"Twilight falls on empty streets,

I've seen it all, the days repeat.

A thousand nights of restless sleep,

I'm losing touch with everything.

So call it off, you can't save me now.

There's nothing left of me to give."

Yes his horns can be broken off (they're similar to obsidian in makeup and, by extension, brittleness) and there's a sort of core to it that has veins flowing (those yellow streaky bits visually map the location of the veins inside) thru so yes if the core is broken they will bleed, but it grows back. Just slower when the core is broken, since it has a lot to heal now.

The first time his horn is truly broken this badly, it was from his father during his childhood (still figuring out who that'll be) but when it breaks again during a fight he gets into in his later years, he's reminded of what his father was, and how much he hated that stryx for what he did to both Mortifer and his mother. He also slowly realizes that he's becoming just like him in the way he acts, treats others, what he does to get what he wants, etc. and it really messes with him after he comes to that realization. So he immediately goes into hiding, away from the world to lie low, but knows there's one old friend he truly needs to seek out and make amends to in the end.