Very soon he becomes a righteous soul, and gets lasting peace. O Arjuna, swear on My behalf that My devotee (one devoted to the Supreme) never perishes.
Krishna adds that such a one, no matter what he has been earlier in his life and ways, soon becomes a righteous soul, deserving permanent peace and quietude.
Often the virtuous people become complacent, even conceited, by their virtuous disposition and the few noble deeds they have done. And this hinders their growth. The constriction continues indefinitely.
Whereas here is one who yearns for purity and the blessedness of devotion. The thought of the misdeeds done, if at all, now urges him to be totally wedded to righteousness and devotion. It leads him to permanent peace – a reward people everywhere aspire for, but are found rarely to win!
Krishna wants Arjuna to swear on his behalf that the devotee of the Supreme never perishes. An assurance many look for and cherish heartily! These assurances and promises make the message dear and valuable!