halacha theory - Halachic base of big loss (hefsed merube)

We see in the halacha many times that when we have a dispute if something is permitted or not and we pasken that it is not permitted, the halacha changes when there is a big loss.

I understand it intuitively, but is there a halachic definition of hefsed merube?

What is the source of it?

When do we apply it?

One example is in Jore Dea siman 69. There the Rema holds that if someone salted raw meat without washing it before, the meat is not kosher. When there is a hefsed merube you may wash it and salt it again.

Answer

Although he claims he didn't invent it, the Ramma was the one who popularized hephsed meruba, so I will quote what he has to say about it, found in his forward to Toras Chatas. This is my rough translation of dibur hamaschil והנה.

And behold I will save myself in one respect so that the reader will not suspect me. For sometimes I will write to be lenient for a large loss or a poor man for an important item, or for the honor of Shabbos. The reasoning is for in those places it seems to me to be completely allowed according to halakha. However, the later authorities were stringent on the matter, I therefore wrote that in a situation of impossibility, we can place the matter on it's law. And so I have found in the early ones and later ones who have done this. The Mahari Minz in his responsa #16 that a poor man throughout the week and a rich man on the eve of shabbos are the same, however, the custom is to tell them the reason (of the leniency) this one because he is poor and this one for the honor of shabbos, so they will not be confounded that at times I disallow and at times I allow.

I would like to point out that this is very different than what many people think hephsed meruba means. They equate it with what is classically called ra'uy lismoch alav bishaas hadchak. Which means we disagree with that opinion but since he is a great rabbi, his opinion is worth something as a halakhic decision. This is hardly ever used in classic codified halakhic works. What the Ramma describes as hephsed meruba is the exact opposite. An opinion who we agree with, but for whatever reason decided not to rule with lichatchila.