"She shall remove the garment of her captivity from upon herself, and she is to dwell in your house, and weep for her father and her mother for a full month. After that, you may join her and possess her, and she may become your wife." (Deut. 21:13)

This is a reference to the soul and its garments acquired as a result of her becoming defiled. The removal takes place by means of eradicating the traces of sins through penitence, self-flagellation, etc.

...one is to confess one's sins...one had committed...against G‑d and the community of Israel...

"and she is to dwell in your house, etc," during which time one is to confess one's sins and weep in sorrow over all the trespasses committed against our father and mother, i.e. against G‑d and the community of Israel whose traditions were flouted.

"For a full month," which is sufficient for this purpose. The Torah may have in mind the Month of Elul which our Sages set aside for penitence prior to the Day of Judgment, Rosh Hashanah.

"After that you may join her, etc." You will then benefit from the soul's spiritual light. This is the mystical dimension of "When someone toils for his soul, he toils on behalf on his true self." (Proverbs 16:26) His soul will then assist him to remain on the correct path.

...this soul will once more inhabit your body...performing the task assigned to it.

"and possess her" - you will have become her master. The reason the Torah describes you as her master is because the moral strength of your actions has rehabilitated her.

Eventually, this soul will once more inhabit your body and perform the task assigned to it. This is what the Torah means with the words, "she may become your wife."

[Translated and adapted by Eliyahu Munk.]