When Hawkeye wakes up in the water in Endgame on Volimer after Black Widow sacrifices herself, why is Hawkeye capable of holding the soul stone? He's just human?
I believe the reason lies in the sentience of the Stones. Each Stone is shown to have a degree of sentience in one form or the other and this can decide the fate of who wields it.
The Space Stone can be described as being temperamental and irritable, reacting easily and this has been referenced multiple times in the MCU.
First is when Red Skull holds it and gets punished by being sent to Vormir to act as guardian to it's “brother”, the Soul Stone.
Next is in Avengers when SHIELD has custody of it, it starts turning on by itself when Loki passes through. Erik Selvig (the doctor that had been working on it) describes as being alive.
(Dialogue between Fury and Selvig in Avengers)
Fury - Is there anything we know for certain?
Erik - The Tesseract is misbehaving.
Fury - Is that supposed to be funny?
Erik - No, it's not funny at all. The Tesseract is not only active, she's… misbehaving.
The Mind Stone is shown to corrupt and manipulate those around it. According to Marvel, the real reason Loki acted so much crazier than usual in Avengers was because he spent so much time around the Stone which made his obsession and jealousy with Thor grow to become much more worse.
We see the Mind Stone's effect later in the film when it's with The Avengers and causes tension around them, leading to Bruce picking up absentmindedly. It was also a major reason as to why Bruce lost control and transformed to Hulk.
The Mind Stone was also what corrupted Stark's and Bruce's program to create Ultron in Age of Ultron.
With this, I see a similarity between the Mind Stone and the One Ring. Both corrupt, twist and manipulate those in their vicinity to protect themselves. Just felt pointing this out.
The Reality Stone in it's “raw” form acts like a parasitic organism that latches onto a lesser host and begins feeding off it's life force till it dies. A more powerful host like Malekith can seemingly control and it ends up being more like a symbiotic relarionship. Although, it just may be that it still feeds off higher beings and it isn't as noticeable but since humans are fragile, they die faster.
The Time Stone seems more docile and tame than it's siblings though that may just be because Strange is a worthy master. Here's a quote from Mordo
Temporal manipulations can create branches in time. Unstable dimensional openings. Spatial paradoxes, time loops! You want to get stuck reliving the same moment over, and over, forever, or not having existed at all?
This shows that in the hands of an unskilled person, the Time Stone could do more harm than good.
The Power Stone is the one that is the least known overall as it spends most of it's time inside it's containment device, The Orb. Apart from the fact that it is known to have enough power to rip planets apart and touching it automatically kills/causes intense pain to the person. So there's not much to go here. We can assume it's not a “nice” stone since all it causes is mostly destruction and pain.
And now for the Soul Stone.
Often described as being the oldest, wisest and most dangerous stone. I believe Soul Stone makes up it's own rules as to who gets to receive it. It makes sense since Red Skull is just the Stonekeeper and there to act as a mouthpiece to whosoever wishes to collect it. The Stone is his “master” and he guards it.
Now, it makes sense that the Soul Stone, being a Stone that can dictate life and death, i.e. can bring back or kill any life in the universe, would want a life that can never be brought back no matter what and even more so that it's the life the user would want to bring back the most seeing as it's the person they love the most. This fits well with the idea that the Stone is the (like I said earlier) oldest, wisest and most dangerous.
I believe the Soul Stone gave itself to Hawkeye and Thanos willingly. A bargain is a bargain and a deal is a deal. The Stone understands and respects that. There's no need to kill it's owner when the deal had been upheld.