nonexist

Probably a back-formation from nonexistent. By surface analysis, non- +‎ exist.

nonexist (third-person singular simple present nonexists, present participle nonexisting, simple past and past participle nonexisted)

1. (intransitive) To not exist; to unexist.
   • 1860, Charles Kittredge True, The Elements of Logic, page 167:

     Nothing is by the laws of the mind to be held as having no beginning, which we can rationally conceive to have once nonexisted and then begun.

   • 1974, Stanisław Lem, translated by Michael Kandel, The Cyberiad:

     The brilliant Cerebron, attacking the problem analytically, discovered three distinct kinds of dragon: the mythical, the chimerical, and the purely hypothetical. They were all, one might say, nonexistent, but each nonexisted in an entirely different way.

   • 1974, John Boyer Noss, Man’s Religions, fifth edition, page 160:

     Like the Buddha, samsara and Nirvana neither exist nor nonexist, nor both exist and nonexist, nor neither exist nor nonexist.

   • 1993, Daniel Kolak, Self, Cosmos, God, page 370:

     Of something that does not satisfy the presupposition of the pair exists and nonexists, and so neither exists nor nonexists, we cannot ask why it exists.