More likely it's a reference to dysentery, which quite literally caused people to have "shat themselves to death" and was a huge problem not only in the real-life Middle Ages but also in books Game of Thrones is based on, where it is called "the bloody flux" (or in Essos after a particularly bad outbreak, "The Pale Mare") and is greatly feared:

Tyrion felt a pang of rage. "You fucking son of a pox-ridden ass," he spat. "I hope you die of a bloody flux."

A Game of Thrones - Tyrion V

As well as fitting the Game of Thrones tradition of showing a realistically grim fantasy version of the Middle Ages full of unpleasant but historically appropriate details, people crapping themselves to death is a big deal in the books and so referencing undignified deaths from dysentery like this is one of the many passing nods the show makes to details from the books.

"...Soon after came the sickness, a bloody flux that killed three men of every four..."

...Ser Barristan frowned. "Your Grace, I have known the bloody flux to destroy whole armies when left to spread unchecked... The bloody flux has been the bane of every army since the Dawn Age..."

A Dance with Dragons - Daenerys V

In the books:

• Ironically, it might be one of the many ways Beric himself died:

  They [Lannister torturers in Harrenhal] learned that Lord Beric had ten starvelings with him, or else a hundred mounted knights; that he had ridden west, or north, or south; that he had crossed the lake in a boat; that he was strong as an aurochs or weak from the bloody flux...

  A Clash of Kings - Arya VI

• I think Beric is the closest we come to a named character in Westeros dying of it, though it's often talked about, mostly as something that effects the commoners. For example, there's an outbreak in the slums of King's Landing, and Jaime and Brienne meet an innkeep in the riverlands whose son died of it:

  We had two sons, but the lions killed one and the other died of the flux

  A Storm of Swords - Jaime II

• Good Man #1 Ser Davos also has a similar near-miss when he is washed up on the shore after the Battle of the Blackwater:

  His ordeal had weakened him. If he stood too long his legs shook, and sometimes he fell prey to uncontrollable fits of coughing and brought up gobs of bloody phlegm. It is nothing, he told himself. Surely the gods did not bring me safe through fire and sea only to kill me with a flux.

  A Storm of Swords - Davos II

• There's a lot of people crapping themselves to death in a major book-only plotline:

  Dany accidentally causes/contributes to a huge dysentery pandemic that sweeps across Slaver's Bay, causing thousands of the good people she liberated to crap themselves to death

• This is then followed by a dramatic scene where...

  ...it really, really looks like Dany has caught it herself and that her entire storyline might literally end with her shitting herself to death in a field

^{Credit to A Search Of Ice And Fire for helping me find the quotes.}

In real life:

It's also a reference that people familiar with comparable real-life history will recognise. Some examples from Wikipedia's "notable cases" list:

• King Henry V of England, whose shitting himself to death in 1422 was an important event in the build-up to the War of The Roses (which the War of the Five Kings is loosely based on)
• King John of England in 1216, the real-life version of the king Robin Hood is supposed to have crossed paths with
• Erasmus in 1536 - an undignified end for a much-loved scholar
• Sir Francis Drake in 1596, a famous seafarer (or pirate, depending on who you ask) who was one of the first sea captains to sail around the world and played a major part in defeating the Spanish Armada. Before shitting himself to death.

So who was it who shat themselves to death?

Whoops, I haven't answered the question yet...

The nice thing about this line is it alludes to three very different types of good people who suffer and are forsaken by the gods, in a way that tells us something about how Sandor's character is evolving:

• The hanged: People like his friend the septon. Most times we've seen people hanged, it's been innocent victims of marauding pillagers (e.g. the women Brienne cut down and buried). It brings to mind the people trying to live their lives being deliberately preyed on by the monsters that awaken when you put a sword in a man's hand.
• The beheaded: People like Ned, who Sandor seemed to respect judging by amongst other things his empathic reaction to Joffrey tormenting Sansa with Ned's head. Most times we've seen people beheaded, they've been victims of politics and the ambitions of the powerful (sometimes their own).
• The shat: The thousands of anonymous people killed simply by the deprivation of a war-torn land. People so lowly in power and poverty we haven't even seen them on screen except as emfeebled extras huddled in the background. It contrasts sharply with the Neds of the world, and it tells us a lot that Sandor isn't just one of the few who even cares to think about these people, he's wondering why the gods too forsake them

It would make perfect sense if Sandor was thinking of some decent, respect-worthy commoner of such modest means they didn't get a name or screen time. Someone like the anonymous innkeeper's son from the books.

Someone similar to the too-trusting farmer and his daughter who Sandor robbed and left to starve and whose house they are now in - but the visibly shaken reformed Sandor can't quite bring himself to reference that directly. If he'd said "or starved in a corner", Beric might say "Like the bodies we found?" and notice how uncomfortable the question makes him. Best not go there. Wait until after dark to bury the bodies, hopefully the others will be asleep and won't ask any difficult questions.

One addition to CyberClaw answer :

He might be talking about the farmer who took him and Arya in when they were on the road.

Yes, Sandor beat him for a bag of silver but it doesn't mean he did not see that generous farmer as a "better man". He merely thought better men like the farmer don't get to live long and bad men like himself make better use of those silvers.

The farmer did die in a field somewhere (because Sandor has probably no clue where the farm was) and as CyberClaw said "people soiling themselves as they die is common."

I found that famine (which the farmer and his daughter were condemned to) has the following effect:

This is one of the causes of the intractable diarrhoea, which is found in so many famine victims.
(source)

Even if you don't believe the Hound doesn't know where to put the farm on a map he might have said somewhere just because he couldn't say in this very field which fits perfectly the "shat themselves to death in a field somewhere".

The farmer was a good man who due to famine was subject to diarrhea in a field which location the hound probably doesn't know the name of and died because of it.

People soiling themselves as they die is common.

So we only need to see what deaths Sandor was present at, and if they match. I can only think of Mycah, the butcher's boy. He was male, and it was in a field, but, I don't think he'd call him a better man due to his young age.

But here is the thing, the way he talks "shat themselves in a field somewhere" makes it sound like he didn't know the exact location, which points to deaths he was not present for, or just probable deaths from his perspective.

He might not know if Arya survived, and odds are, a girl so young met her untimely end when left alone. Although she is a girl so it doesn't fit the "man" part.

He might be referring to the rightful heir to the throne, Stannis Baratheon who died at the end of Brienne's sword in a field after losing a battle.

He might know of Jon Snow's death as commander of the night's watch.

He might have heard of the mutiny against Jeor Mormont.

He might have heard of Barristan Selmy's demise. He knew him while serving the king.

Tywin Lannister was killed in the privy while shitting, but not on a field.

Maybe he was referring to the Viper. Since it'd be connected to him in a way. He'd be rooting for his victory against his brother after all.

It's hard to tell exactly who he meant, even if anyone in particular or someone's death we witnessed.

I believe this is actually part of the importance of this particular scene to the development of Clegane's character.

While the first two deaths referenced are easy to pin to specific persons (Brother Ray and Ned Stark, respectively), the third seems as though it is a reference to an unnamed soldier (or possibly more than one, although based on the previous references I suspect Clegane, at least, has a particular soldier in mind) alongside whom he once fought (who, as mentioned by others, would have died of dysentery, based on the description).

This tells us that the Hound is capable of recognizing goodness not only in holy men and powerful men, but in base, common men that we the audience would not even be expected to notice in the background, and who likely only displayed their character in small, relatively insignificant ways (i.e., smaller ways than being a just and fair lord or leading a group of strangers in the ways of peace).

You're assuming that he's thinking about specific people. This isn't necessarily true.

Remember that this is a brutal, violent world. For "beheaded", I'm sure you're thinking of Ned Stark; but it could just as well apply to Robb, Rickard Karstark or Rodrick Kassel. Executions happen all the time, whether for actual crimes or simply for being on the losing side. So the Hound will have seen any number of commoners hanged, and a fair number of nobles beheaded.

As for "shat themselves to death in a field", even if we assume he's talking literally, this is a world without any particular medical knowledge and there are plenty of diseases which would cause that - typhoid or cholera, for example. It's quite likely he's talking metaphorically though and simply referring to people dying on the battlefield.

Does Clegane think any particular person is better than Dondarrion? Most probably not, but Clegane doesn't really respect people anyway. He shows that lack of respect by comparing Dondarrion to executed criminals and plague victims. And Dondarrion himself wonders the same thing - why he is any different.

Is it possible that he was referring to himself? We can logically assume he didn't die after his battle with Brienne, but we know he was very near death. He probably should have died and if he had, the Lord of Light wouldn't have brought him back... right?

As he laid on the stone in that field, he was unable to move for any reason, including bodily function. He would have sat with that stench interrupting his thoughts as he looked over the field dying, humiliated. Did he deserve that? Perhaps, he recognized that he had done terrible things, but had also done some good things as well. Maybe he was saying, "So why does the Lord of Light keep bringing you back? Brother Ray was better than you. Ned Stark was better than you. Hell, I'm better than you. If I had actually died, would he have brought me back?". He is trying to understand why and what earns you that right...