Ajāmila has already atoned for all his sinful actions. Indeed, he has atoned not only for sins performed in one life but for those performed in millions of lives, for in a helpless condition he chanted the holy name of Nārāyaṇa. Even though he did not chant purely, he chanted without offense, and therefore he is now pure and eligible for liberation.
Srimad Bhagavata Purana
श्रीमद्भागवतमहापुराणम्
मूल श्लोकः
अयं हि कृतनिर्वेशो जन्मकोट्यंहसामपि । यद्व्याजहार विवशो नाम स्वस्त्ययनं हरेः
ayaṃ hi kṛtanirveśo janmakoṭyaṃhasāmapi | yadvyājahāra vivaśo nāma svastyayanaṃ hareḥ
SB 6.2.7