It's grammatically correct. I saw your earlier question about "he the shot dead," and I was trying to think of how to explain why it's different from Rand's title. I think the main difference is just that your example is singular, and Rand's is plural. Certain adjectives can become nouns when you put "the" in front of them. The noun form then refers to all the people or things that can be described by the adjective. Normally, "living" is an adjective, but when you say "the living," it means "those who are living" or "living people." The word "dead" can also work this way: "the dead" means "the people who are dead." It's perfectly natural and common to say things like, "We should respect the dead." "The injured were sent to the hospital." We usually use this kind of structure with words that obviously refer to people, but in literary or poetic language, you can also say things like "the forgotten" or "the lost," where it's not totally clear whether the phrase refers to people who are forgotten/lost, or things that have been forgotten/lost. In either case, though, the noun is plural. "The forgotten" means either "forgotten people" or "forgotten things." It can't just mean one forgotten person. The other problem with "the shot dead" is that we just don't really ever use this form with an extra modifier. "The dead" makes sense as a plural noun, but "the shot dead" doesn't. There are exceptions -- you could say "the severely injured" instead of just "the injured." But in most cases, it sounds very weird to put a modifier after "the." "We the living" is good and even rather poetic. "We the still living" sounds terrible. I don't really know why this is the case, but it's the best explanation I can give.

There's a book titled "We the living" or There's a book called "we the living" or "there's a book named "we the living" the book is called/titled QUOTE "we the living" so you need to QUOTE it with single or double QUOTATION MARKS. To put a comma in the QUOTED TITLE 'we the living' is incorrect. YOU HAVE CHANGED THE NAME=TITLE of the book to "we, the living" this is not what the Author titled the book. Unless my internet searches have given me wrong information but then the same rules apply "there is a book titled ' -----' or there is a book the tile of the book is " ---- ----"

The book title is fine (in my opinion, of course). There is no call for a comma. In your example, "the living" is not non-essential information ; it clarifies the aspect of "we" that the writer wants to concentrate on. If you'd like more about use of the comma you could look at https://www.thepunctuationguide.com/comma.html#mechanicalusesofcomma

It would be more grammatically correct to have a comma after we - as in "We, the living." But as a book title it works.

The same structure of wording appears in the US constitution. That type of phrase isn't exactly common. I can see the thought process behind your question.