Ok, I did try my best to search around to see if this was posted before. So far no luck, maybe I suck at searching? But I swear I did my best, my apologies if this was already discussed, please don't get mad at me, its the first time I am posting and I also was hesitant to do so.
Anyway, after much deliberation, I am going to explain exactly what happened to the best of my ability.
I have started to hunt, I used to play back in World 4 when you used to be able to hunt with a sling and stones on the river and make signposts to trap animals. I've read around already how that isn't quite viable anymore, also, had a hard time getting accustomed to new system, still arrows and bow aren't quite my thing but I digress.
I was hunting down the river, have gotten a few foxes, have yet to kill a boar, and I have to defeat a swan for credo quest. But recently I decided to try my luck and go for a bear, luck was on my side since I actually found one near the river, however I didn't have enough arrows, to be honest I don't know how much HP they have but I decided to try anyway, after a few arrows the bear runs away, bummer, I circle around the little peninsula he was at, find it again, shot a couple more of arrows, run away. I was doing like 64 damage average. But once I ran out of arrows the last arrow didn't hit and the bear was still aggroed by me. It's usual for an animal to bleed if you are hunting it, but this bear was "bleeding" and chasing me, I was on the boat so I was safe. So I decided to make it chase me all the way down the river, and kept noticing how it wouldn't stop bleeding. Decided to try if it would eventually die and to my surprise, it did. I didn't keep track of the time, but the wounded bear would eventually die because it kept chasing me instead of me chasing it. Quality was terribly low though, I am not sure if that was because I am as low or it dying that way. So thats how I got my first bear tooth and bear hide.
I am not sure if this will work on any animal, I mean deers heal. There was no deers around so that helped me.
Edit: I think that it did affect the quality a lot, since projectiles affect the animal quality so a bear dying that way will be of really low quality me thinks.