“pas” or “point” may be omitted in the negative form because “ne” is the simple negative operator, like “not” in English. “ne pas” or “ne point” originally mean “not a step” or “not a point“, meaning “not even a single step” (or point), the step and the point being the smallest units of distance(“pas“) or surface(“point“) possible, so “not even one” stresses zero.

Of course, after centuries, “pas” seems to mean “not“, but it’s not its real sense, and this is why the familiar form without “ne” (example: “j’ai pas faim“) is not correct.

You’re right to notice that we use “pas” almost every time in the current language, but theorically, we may omit it, and this is frequently found in literature or poetry.

DISCLAIMER: I misunderstood the question and the following answer is an explanation about the second "ne" in: "ce qui n’empêche qu’il ne soit chez lui ici".

It is actually a "ne explétif" (full article explaining its use):

Son emploi ne modifie pas la phrase positive en une phrase négative.

EN: its usage does not turn the positive sentence into a negative sentence.

This kind of "ne" can be used in many cases, one of which being this specific case:

La phrase principale est positive ou négative, et contient un verbe exprimant l’évitement, l’empêchement, la défense, la précaution (tel que : empêcher, éviter, prendre garde). Marivaux s’exprime de la sorte […] : « Tout ce que je dis là n’empêche pas qu’il n’y ait de jolies choses dans votre livre… »

EN: The main sentence is positive or negative, and contains a verb expressing avoidance, defense or caution. Marivaux uses it the following way: « Tout ce que je dis là n’empêche pas qu’il n’y ait de jolies choses dans votre livre… »

The full quote from Michel Serre is the following:

Tout le monde vient d’ailleurs, ce qui n’empêche qu’il ne soit chez lui ici. Il n’y a pas d’étrangers et nous le sommes tous. Ici est partout, il n’y a que des ici.

Rough English translation: Everyone comes from another place, which does not prevent anyone from being home here. There are no foreigners and we are all foreigners. Here is everywhere, and everywhere is here.

He is trying to express the idea that we are all foreigners compared to someone else, and therefore there is no such thing as "a foreign place". That’s why whatever the origin, everyone is at home anywhere.

The second clause “n’empêche” is indeed negative. (And the third clause “ne soit” isn’t, this one is a ne explétif.)

There is no particular set of verbs with which the “ne littéraire” can be used. The word ne alone can convey negation when paired with any verb in very formal French. You can generally expect philosophical texts to be written in very formal French, and Michel Serres is no exception.

It’s true that some verbs or constructions are more likely to be negated with only ne. I would put empêcher among those verbs. “Ça n’empêche” or “il n’empêche” or even “n’empêche” is a moderately common colloquial idiom where pas is omitted: it’s a whole sentence or whole clause meaning roughly “I’ve heard what you said, but nevertheless, there is contradictory evidence”, which can be translated in English as “nevertheless” or “even though”. In Serres’s sentence, given the formal register, any verb could have been negated without pas, but with the verb empêcher it flows more naturally than with most.