Elsie: "Can you explain (or link to an explanation) to help this PROTESTant understand how this process of self-cleansing works?"
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Obviously, the part humans have to do to be cleansed from their sins is to confess them (like "Salvation" and the Bible said). (That's what the "Sacrament of Reconciliation" is -- confession.)
God gives us a definite part to do for ourselves.------------------------------------------------------------
If we confess our sins, he is faithful and just, and will forgive our sins and cleanse us from all unrighteousness. 1 John 1:9
"If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained." 1 John 1:9------------------------------------------------------------
God's written Word tells us sinners that we must confess our sins, and God will forgive us, and clearly, that confession is what the sinner's own part involves in obtaining their cleansing from their sins.
(God often chooses to delegate various necessary actions to human beings, which they then have to freely choose to do within their own free will which God gives them. We cannot do those things by ourselves, of course, and Catholics fully recognize that, but when you get right down to it, we actually cannot do anything by ourselves. You have to breathe to stay alive, and you may say that your are keeping yourself alive partly by breathing, but you cannot take one single breathe by yourself without God willing it be possible, and you cannot stay alive or even exist for one single yoctosecond on your own, without God willing it be so. God does His part, and He expects us to do our part.)