After defeating Sarkoth and showing his claw to Hana'zua, your actions have given him the energy to keep on fighting. But he cannot make it to the Den without help and asks you to tell Gornek of his situation.
Seeing the deed you have done for me steels my heart. I cannot fall so easily! I must endure!
After you accept the quest:
Hana'zua says: Go Swiftly, <name>. My fate is in your hands.
From your description of the beast, I believe you must be speaking of Sarkoth! It is no wonder that Hana'zua was overtaken by it. Aid will be dispatched to him immediately, trouble yourself no more with Hana'zua's plight.
However, I must say, I am most impressed to hear that you brought Sarkoth to death. It is a feat to be proud of, <name>. And that you would fight for a stranger's honor, while other tasks occupied their time, your own honor is heightened.