Is not a term Paul used, but one that only Jesus and Peter used, both of whom were speaking DIRECTLY to the nation of Israel.
will never fall away and lose his soul,
There is currently no such thing today (nor for the past 1800 years or so) as a "born again believer," despite the fact that the church has misappropriated the term to refer to Christians. It does NOT refer to Christians, but rather, believers under the New Covenant meant only for the House of Israel.
but lots of fake believers and double-minded pretenders will.
As Paul said:
In Him you also trusted, after you heard the word of truth, the gospel of your salvation; in whom also, having believed, you were sealed with the Holy Spirit of promise,who is the guarantee of our inheritance until the redemption of the purchased possession, to the praise of His glory. - Ephesians 1:13-14
http://www.biblegateway.com/passage/?search=Ephesians1:13-14&version=NKJV
Does "sealed with the Holy Spirit of promise who is the guarantee of our inheritance until the redemption of the purchased possession" mean nothing to you?
When a Christian is saved he is filled with the eternal Spirit of God that will never leave him or forsake him. A tentative 'believer' who never fully commits and does not get saved does not get filled and sealed with God's Spirit.
When someone becomes a Christian, they are sealed.
People who are not Christians are not sealed.
God is just and will sort out the rest.
A sinner can clean himself up
A sinner cannot clean himself up. Hence the need for a Savior.
but if God does not come in to save him and make him clean he is still unclean in God's eyes.
Matthew 12:43-45
King James Version
43 When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none.
44 Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished.
45 Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Even so shall it be also unto this wicked generation.
Did you notice that you're quoting from Jesus, who was speaking to Jews, and not Gentiles? And not only that, it's a passage I would expect a Charismatic to use, as it's speaking about spirits, not humans.
The passage you quoted has nothing to do with the Body of Christ, who is not "cleansed", but put to death, and buried. He's a new creation, old things have passed away.
Completely different than "cleansing."