If a believer backslides into sin and they refuse to repent of it, they are not saved during the time they are backslidden. God's grace does not cover any kind of rebellion done against Him.
But the Bible picture of salvation is so totally different. First of all it is the consequence of God's grace, that is, His active unmerited love and favour. As we become aware of God's saving activity being carried out towards us solely due to His unmerited love and favour we respond by believing. It is all God's work, we simply accept it by faith (by recognising His gracious work and saying thank you).
'By grace (God's unmerited love and favour) you have been and are now saved (perfect tense) through faith, and that salvation is not of yourselves IT IS THE FREE GIFT OF GOD not of works lest any man should boast.' (Eph 2.8-9)
Note WE HAVE BEEN SAVED as a free gift, not as a loan. Jesus Christ is now our Savior. It happened in the past and it continues to the present. There is nothing more for us to do. From now on it is His work. A licence to sin? Nonsense. God has dealt with that too. 'For we are created in Christ Jesus UNTO good works which God has before ordained that we should walk in them' (verse 10). God is at work in us to will and do of His good pleasure (Phil 2.13).
Salvation is God's work not ours, and it includes having the guilt of sin removed from the start (Rom 4.5), (we have been saved), God continually working in us 'bringing us from one degree of glory to another' (2 Cor 3.18), we are being saved (1 Cor 1.18); AND THE GUARANTEE THAT HE WILL FINALLY PRESENT US PERFECT BEFORE HIM (EPH 5.25-27).
It is all His work. We simply respond in love and gratitude.