In general, how does price relate to quality?

At any given price, once you find the best component at that price the next better one will cost more. That's the relationship. 

When you find the best component at any given price, and there is a better one but it costs 2x, 3x or more, that is a contender for giant killer. When it sounds good enough there are people who find it competitive with some of the very best regardless of price, then you definitely have a giant killer. 

yes, there is some great low cost stuff, some not so good high cost stuff, of course the issue of component matching...though I have always found the gear I like the best costs more...

There is a strong correlation between price and sound quality, but it's definitely not 100%. Many lower priced components outperform similar more expensive components. It's worth noting that price is always influenced by factors such as mark up, labor costs, shipping, taxes/tariffs etc. so a higher price does not automatically mean a better design and better components.

In addition, "sound quality" is rather vague as it is subjective, and that also plays into this.

That said, those who claim their $2 flex sounds the same as a $2,000 cable is either totally disingenuous and/or deaf, and that is why you will see the same tiresome individuals making such claims. What's notable about their claims as they never explain their findings in terms of listening to the cables, but always in the context of their 4th grade understanding of science and psychology.

Budget audiophiles desperately need "giant killers " in a vain attempt to offset the fact that they are nowhere near SOTA. They need to believe whatever they use is a giant killer. It's the culture of the price-obsessed listener.  :)