Ne was the original negative particle and is still present on its own in certain fixed expressions, like je ne sais quoi.

In more recent usage (compared to the 12th-century grammaticalization of pas, Voltaire is recent!), it doesn’t strike me as random, but rather poetic.

It can still be used today with a similar effect; compare its appearance in « Beau comme le soleil », a song from the 1998 musical Notre-Dame de Paris:

Quand il me serre contre lui

je voudrais fuir, mais je ne puis.

Here the use of puis instead of peux also reflects the elevated register of a lone ne.

Another theory I might propose for that particular usage of Voltaire’s is that de ta vie could function as a sort of grammaticalized negative particle. That is to say, if jamais can complete ne in place of pas, then it’s conceivable that de ta vie, which has a similar meaning, could do so too. There is quite a variety of items that can fill that slot, and the Banque de dépannage linguistique article that Laure links to below shows de sa vie being used in the same way:

Il n’a de sa vie imaginé qu’il serait un jour un héros.

But I’m not quite sure I’m interpreting the Voltaire sentence correctly, since the structure could be approcher quelqu’un de X instead of de ta vie being temporal. Also, in Laure’s catalogue below and in the links cited, it’s not clear that this phenomenon would be at home in the imperative mood.

Until the 17th century ne on its own was enough to negate a verb and pas was optional. The use of ne isolated (without the negative adverb) can still found in Classical French (Voltaire, La Fontaine, Molière, etc.) but except in a few cases it has become quite rare nowadays. Nowadays it is the opposite, there is a tendency – mainly in oral language (but nobody knows what the norm will be 200 years from now) – to drop ne that has lost part of its negative content and to use pas (or other negative adverb, jamais, plus, etc.) alone.

When can ne be used alone nowadays?
In Modern French ne can be used alone only in a limited number of cases. The omission of pas is not compulsory, it is considered literary, more or less literary according to frequency.

• With the verbs cesser, oser, pouvoir, savoir when followed by an infinitive. It is probably the most frequent case.

  • Il ne cesse de me harceler pour savoir quand je vais venir.
    Je ne peux/puis te le dire maintenant.
    Je ne saurais dire pourquoi.

• With the verbs daigner, manquer it is also possible but less frequent.

  • Il ne manque de me rendre visite à chaque fois qu’il vient en France.

• In a conditional clause starting with si. Quite literary.

  • Il ne pouvait pas s’endormir si je ne l’avais embrassé. (René Bazin De toute son âme – 1897).
    This is very literary, and most people will use pas. It is more frequent though in the phrases: si je ne m’abuse, si je ne me trompe.

• In negative questions with an affirmative meaning starting with qui. Quite literary.

  • Qui ne rêve de faire un jour le tour du monde ?

• When the verb is followed by an adverbial phrase of time meaning jamais. Quite literary.

  • Je n’ avais de toutes ces années pensé que je reviendrais en France.

Ne is always used alone in some fixed phrases: qu’à cela ne tienne, n’avoir de cesse, ne dire mot, il n’importe, on ne peut plus [plys], on ne peut moins, on ne peut mieux, etc.

For reference:

• Sentential Negation in French (Paul Rowlett, 1998)

• BDL

  • Ne pouvant être employé seul
  • Ne employé seul

• l’adverbe ne employé seul (Bertrand Boutin)

• Literary and formal negative structures (thoughtco.com)