The word pereciese is the imperfect subjunctive form of perecer in the first person singular. There are other translations for this conjugation.
See the full perecer conjugation
Aun estaría con ellos en un programa de cansadora y desgastante jornada por el desierto hasta que la generación entera de no creyentes pereciese.
He would still be with them in a program of weary, protracted wilderness wanderings until the entire generation of unbelief had perished.
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