I'm going to give my perception as an “ordinary” native (of France). Specialists of French language, French language history and French teaching may have a different point of view.
I've never heard of this list of seven verbs (cesser, oser, pouvoir, bouger, daigner, manquer, savoir), and they don't strike me as more likely to admit “ne” as the sole negation than other verbs. I don't think the verb has any influence on the choice of negation, except that verbs that belong strictly to informal language and wouldn't be used with “ne” alone. I can't find any web page in French that mentions this list either; it seems to be strictly a French as a second language thing.
The sentence you cite has many elements that make it not only literary but somewhat old-fashioned, especially in combination:
- Use of the conjunction quoique: modern French tends to prefer bien que).
- Use of the subjunctive past fussent: the subjunctive past is a hallmark of high register that does not belong in the language of the man in the street.
- Use of “ne” as the sole negation: apart from a handful of set phrases, this is not done in ordinary speech or writing.
- Use of “jusque” with a meaning that is not related to time or space: this is rather on the formal side.
- The word order “n'oublier jamais”: modern French prefers “ne jamais oublier”.
- Use of “il est” to mean “there is”: modern colloquial French solely uses “il y a”, whereas very high-register French tends to eschew “il y a”.
- Use of the verb “s'estomper”, which is slightly old-fashioned.
- The sheer construction of the sentence, with the two linked negations: “il n'est jusqu'aux X que P qui ne V” to mean that no X does V, not even those that P.
Note that it would not be possible to add “pas” to the first negation. It would be possible if the sentence was expanded:
il n'est pas de souvenirs, jusqu'à ceux que l'on s'était juré de n'oublier jamais, qui ne s'estompent pas au fil des ans.
But when the mention of memories is condensed, adding pas would cause the negation to be about the clause starting with “jusque” instead of being about the verb est meaning existence, which would invert the meaning of the sentence. Yes, it's a bit complicated.
For reference, this is how that fragment would be written in everyday French:
il n'y a pas de souvenirs, jusqu'à ceux que l'on s'était juré de ne jamais oublier, qui ne s'estompent pas au fil des ans.
And this would be considered clumsy (“lourd”) due to the double negation, so the sentence would probably be recast to something like
tous les souvenirs, y compris ceux que l'on s'était juré de ne jamais oublier, s'estompent au fil des ans.
But this formulation completely lacks the charm of Jean Sola's sentence.
As for the name, “ne littéraire” also seems to be a French as a second language thing. I don't remember a special name from my high school days, and the French Wikipedia article just uses the descriptive phrase “emploi de « ne » seul”.