The distinction between this word and the simple εἶναι, to be, is very subtle. The verb ὑπάρχω originally means to make a beginning; hence, to begin or to come into being; and, though used substantially as a synonym of εἶναι, of a thing actually existing and at hand, it has a backward look to an antecedent condition which has been protracted into the present. Thus we might paraphrase here, “If a brother or sister, having been in a destitute condition, be found by you in that condition.” Εἶναι, on the other hand, would simply state the present fact of destitution. See on 2Pe 1:8.
Destitute (λειπόμενοι)
Lit., left behind; and hence lacking, as Rev. Compare Jam 1:4, Jam 1:5. This usage of the word occurs in James only.