I think that Pharis was an all around badass to have ranked along side Gough.
Now think about it, if Gough was using a larger, more powerful bow, and had the Hawk ring, and Pharis was on par with his skills, then Pharis wouldn't have been killed so easily by a mere stalker, in my opinion.
Pharis probably is very old, as well. I don't think that archer was around when Pharis passed away. Pharis was most likely not undead, as the game says that "He WAS human". Past tense leading towards the fact that he has died, unless it means that he has become undead and is no longer human. Undeads are refered to as man, but not human. That might take a bit of speculation.
The first thing we need to think of, is where he originated from.
What country/province was known for it's archers?
The Bow and Arrow was one of the most remarkable and scientific weapons of that time, besides maybe the crossbows. What places do we know of, that made simple yet remarkable pieces of machinery and weaponry and spells?
Oolacile, and Astora.
Both of these places were known for their achievements in certain fields of science and magic.
Where do we find the gear, and Hawkeye gough?
Darkroot forest AkA Oolacile.
The Knights seemed to really like Oolacile, we find three out of four of them there. It would be no surprise to say that Hawkeye Gough and Pharis competed here.
Pharis's legend was most likely started when the dragons were still very potent in the world, where they both shot their fair share, and in a time span from then to now the legend could have been altered, to make it seem like Gough challenged Pharis and Oolacile, why else would they be discriminant of him and lock him up?
Humans are the obvious bottom of the social food chain in lordran, so it would be no surprise that a giant would have his discrimination against humans as well.
"Humans…hmph…" - Hawkeye Gough
So if Pharis was the almighty legend who we know, who ranked along side the captain of the dragonslayer archers....
How did he die?
I think that he passed on naturally, and his armor and weapon were passed down through the family. When the abyss struck the family most likely fled, because the weapons were not found there in past time. But they returned later on. And that is how the hat turned up with the Female Archer.
Perhaps Pharis was never real, maybe the player is Pharis.
Hawkeye Gough never knew your name, he could have given you a word translated from his language if giants had a native language. You killed one of the most ferocious of the ancient dragons, with his help.
Of course he would say you're an equal.
What if you killed Gough though?
"Time is distorted in Lordran, heroes centuries old have phased in and out."
It could have been someone else as well. History in lordran repeats itself, Quite literally in fact.
This one has no facts whatsoever, and changes a bit of my previous speculation.
Pharis may just be a children's story with no origin, and could have been used to control certain people.
There have been times were people used false legends to manipulate large amounts of people.
-COUGH- Frampt -COUGH-
Pharis's bow is nothing to brag about, it has no special abilities whatsoever, has a longer range, and does a decent amount of damage. But the longbow is about equal to it. Pharis was human, not superhuman. He could not have ranked along side gough with that bow, there is no possible way that that little bow could shoot farther and stronger than gough's.
Gough shot a moving dragon, while he was blind.
Pharis had to have been using a dragonslayer greatbow if he was real, and his black bow could have been for smaller targets.
-End of Speculation-
Gough was most likely shamed for being equaled by a human, so maybe Gough did something about it.
Here is my list of possible deaths for him
1. He passed away normally.
2. Gough killed him in a battle.
3. Pharis never died, he is undead and is somewhere in lordran.
I don't think that the bandit in the woods was any match for Pharis.
This speculation wasn't very organized as I got different ideas while I typed it and looked things up, but w/e piece it together as you will.
NOTE: Pharis does not = Archer in woods.
"HE was human" -Pharis Bow description