exile
v.
c.1300, from Old French essillier "exile, banish, expel, drive off" (12c.), from Late Latin exilare/exsilare, from Latin exilium/exsilium "banishment, exile; place of exile," from exul "banished person," from ex- "away" (see ex-) + PIE root *al- (2) "to wander" (cognates: Greek alaomai "to wander, stray, or roam about"). In ancient times folk etymology derived the second element from Latin solum "soil." Related: Exiled; exiling.
n.
c.1300, "forced removal from one's country," from Old French exil, essil (12c.), from Latin exilium "banishment; place of exile" (see exile, v.). From c.1300 as "a banished person," from Latin exsul, exul.
Several etymologies are possible. It might be a derivative of a verb *ex-sulere 'to take out' to the root *selh- 'to take', cf. consul and consulere; hence exsul 'the one who is taken out'. It might belong to amb-ulare *-al- 'to walk', hence 'who walks out'. It might even belong to *helh-, the root of [Greek elauno] 'to drive': ex-ul 'who is driven out' [de Vaan, "Etymological Dictionary of Latin and the other Italic Languages"]