You're speaking of a person professing to be a believer, but evidence
seems to be to the contrary. (I say
seems emphatically because there is the possibility one in such a state will show evidence of salvation at some point).
Here is a biblical example of this written in the 1689 LBCoF:
3._____ And though they may, through the temptation of Satan and of the world, the prevalency of corruption remaining in them, and the neglect of means of their preservation, fall into grievous sins, and for a time continue therein, whereby they incur God's displeasure and grieve his Holy Spirit, come to have their graces and comforts impaired, have their hearts hardened, and their consciences wounded, hurt and scandalize others, and bring temporal judgments upon themselves, yet shall they renew their repentance and be preserved through faith in Christ Jesus to the end.
( Matthew 26:70, 72, 74; Isaiah 64:5, 9; Ephesians 4:30; Psalms 51:10, 12; Psalms 32:3, 4; 2 Samuel 12:14; Luke 22:32, 61, 62 )
All true converts endure, or, are preserved/persevere to the end. It is the evidence they are born from above.
Now you are making things appear prescriptive, that is, if a person then begins to do works they will now be saved as if
"Oh, I better start having some good works if I want to make it in" were the answer to the condition of the soul. That may not be your intent, but that is the conclusion. There is a fine line, we must tread cautiously here as to not misspeak or be unclear.
And this is the problem of the day, we focus too much on "entering heaven some day", effort to get there when in reality we need to seek evidence of conversion.
With all due respect you're conflating evidences of true conversion and making them prescriptive rules one must do to gain heaven. This is, at the least, where you and I may differ.