Sometimes people think that once a person has performed sinful acts, especially acts that are grievously sinful, he must be regarded as a sinner forever. This notion runs contrary to Vaishnava philosophy.
As stated in Srimad-Bhagavatam (6.2.8–10) about the sinful Ajamila:
etenaiva hy aghono ’sya krtam syad agha-niskrtam
yada narayanayeti jagada catur-aksaram
stenah sura-po mitra-dhrug brahma-ha guru-talpa-gah
stri-raja-pitr-go-hanta ye ca patakino ’pare
sarvesam apy aghavatam idam eva suniskrtam
nama-vyaharanam visnor yatas tad-visaya matih
[The Visnudutas said] Even previously, while eating and at other times, this Ajamila would call his son, saying, “My dear Narayana, please come here.” Although calling the name of his son, he nevertheless uttered the four syllables na-ra-ya-na. Simply by chanting the name of Narayana in this way, he sufficiently atoned for the sinful reactions of millions of lives.
The chanting of the holy name of Lord Visnu is the best process of atonement for a thief of gold or other valuables, for a drunkard, for one who betrays a friend or relative, for one who kills a brahmana, or for one who indulges in sex with the wife of his guru or another superior.
It is also the best method of atonement for one who murders women, the king or his father, for one who slaughters cows, and for all other sinful men.
Simply by chanting the holy name of Lord Visnu, such sinful persons may attract the attention of the Supreme Lord, who therefore considers, “Because this man has chanted My holy name, My duty is to give him protection.”