In plain words
Taking refuge in this jñāna and attaining oneness with My own nature, they are not born even at creation nor disturbed at dissolution.
Word for word
Having resorted to this jñāna, having attained oneness with My nature, even at creation they are not born, and at dissolution they are not distressed.
इदं ज्ञानमुपाश्रित्य मम साधर्म्यमागताःसर्गेऽपि नोपजायन्ते प्रलये न व्यथन्ति च
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
अस्याश्च सिद्धेः ऐकान्तिकत्वं दर्शयति —
इदं ज्ञानं यथोक्तमुपाश्रित्य, ज्ञानसाधनम् अनुष्ठाय इत्येतत् , मम परमेश्वरस्य साधर्म्यं मत्स्वरूपताम् आगताः प्राप्ताः इत्यर्थः । न तु समानधर्मता साधर्म्यम् , क्षेत्रज्ञेश्वरयोः भेदानभ्युपगमात् गीताशास्त्रे । फलवादश्च अयं स्तुत्यर्थम् उच्यते । सर्गेऽपि सृष्टिकालेऽपि न उपजायन्ते । न उत्पद्यन्ते । प्रलये ब्रह्मणोऽपि विनाशकाले न व्यथन्ति च व्यथां न आपद्यन्ते, न च्यवन्ति इत्यर्थः ॥ २ ॥
In plain words
And now he goes on to show just how absolutely certain this attainment really is.
What does it mean to 'resort to this knowledge'? It means actually practicing the means that lead to it, not just hearing about it. And what does someone gain by doing so? They come to share My very nature, the Supreme Lord's own nature — not some pale resemblance to it, but that nature itself. This word 'sādharmya' isn't talking about two separate things that merely happen to share some qualities; in this teaching, there simply is no real difference between the knower of the field and the Lord to begin with. This whole promise of a result, by the way, is offered here as praise — to make this knowledge feel worth pursuing. And what does that praise actually promise? That such a person is never born again, not even at the grand moment of creation, and is never disturbed, never shaken, never destroyed, not even when the universe itself dissolves at the end of Brahmā's cosmic day.
Close to the Sanskrit
And he shows the absolute certainty of this accomplishment —
Having resorted to this knowledge, as already described — that is, having practiced the means to that knowledge — this is the sense: they have come to, attained, sameness of nature with Me, the Supreme Lord, that is, the very state of My own true nature: that is the meaning. But 'sādharmya' does not mean the mere sharing of properties, since a difference between kṣetrajña and Īśvara is not accepted in the Gītā's teaching. And this statement of a fruit is made for the sake of praise. Even at creation, at the time of creation, they are not born, they do not arise. Even at dissolution, at the time of Brahmā's destruction, they are not disturbed, and do not fall into disturbance, and do not perish: that is the meaning.