I think I posted a link to this piece by Albert J. Nock previously, but I can't remember so I'm doing it again. Here Nock defines who the Remnant is:
In the year of Uzziah's death, the Lord commissioned the prophet to go out and
warn the people of the wrath to come. "Tell them what a worthless lot they are."
He said, "Tell them what is wrong, and why and what is going to happen unless
they have a change of heart and straighten up. Don't mince matters. Make it clear
that they are positively down to their last chance. Give it to them good and strong
and keep on giving it to them. I suppose perhaps I ought to tell you", He added,
"that it won't do any good. The official class and their intelligentsia will turn up
their noses at you and the masses will not listen. They will all keep on in their
own ways until they carry everything down to destruction, and you will probably
be lucky if you get out with your life."
Isaiah had been very willing to take on the job -- in fact, he had asked for it -- but the prospect put a new face on the situation. It raised the obvious question: Why, if all that were so -- if the enterprise were to be a failure from the start -- was there any sense in starting it?
"Ah," the Lord said, "you do not get the point. There is a Remnant there that you
know nothing about. They are obscure, unorganized, inarticulate, each one rubbing along as best he can. They need to be encouraged and braced up because when everything has gone completely to the dogs, they are the ones who will come back and build up a new society; and meanwhile, your preaching will reassure them and keep them hanging on. Your job is to take care of the Remnant, so be off now and set about it".
What do we mean by the masses, and what by the Remnant?
As the word "masses" is commonly used, it suggests agglomerations of poor and
underprivileged people, laboring people, proletarians. But it means nothing like
that; it means simply the majority. The mass-man is one who has neither the force
of intellect to apprehend the principles issuing in what we know as the humane
life, nor the force of character to adhere to those principles steadily and strictly as laws of conduct; and because such people make up the great and overwhelming
majority of mankind, they are called collectively "the masses". The line of
differentiation between the masses and the Remnant is set invariably by quality,
not by circumstance. The Remnant are those who by force of intellect are able to
apprehend these principles, and by force of character are able, at least measurably,
to cleave to them. The masses are those who are unable to do either.