I also would like to point out that ninja's sword to a bear is like a small swiss arm knife to a human being.
If someone stabs you with a swiss army knife in the stomach or limbs. It's not gonna kill you for many minutes. And the bear only needs like 10 seconds in the already-engaged melee combat to totally annihilate ninja after the stab.
Let's visualize what would really happen:
1. The 800 lb bear charges toward the ninja
2. The ninja skillfully slashes the bear, severly injuring the bear.
3. The bear does NOT INSTANTLY stop, let alone death.
4. The ninja is now at full melee distance with the bear.
5. The bear may bleed like crazy but only thing the bear needs is a single 800lb blow to ninja's body
5. The ninja is dead, dead, dead.