For a second I was worried...

...that this would be about quartodecimanism.

Less arcane answer: This is partly, or maybe completely, a language issue. The typical exposition is that nothing we do can earn us salvation because Christ earned that for all by dying on the cross. It's also claimed that salvation is through grace alone and not works; though the Lutherans and some others will say, through grace and faith alone.

When the seeming paradox is posed, of an apostate, wife-beater, child-abuser, drunkard, etc. being securely saved, the usual answer is that no one who accepted their salvation would act that way; and if they did, it would just show that they were fake believers.

Here's why I say this is a language issue: To claim that you are securely, eternally saved no matter what...as long as you accept that salvation, means that you have to apply the mental process of acceptance, which is in itself an action. My feeling is that one should not say that salvation is something given outside of human agency and then say that each individual human needs to accept it, because cogitating that acceptance is a voluntary act of human agency.