The Alter Rebbe explains that every Jewish soul, even the most wicked, possesses a divine neshamah that is literally 'a part of God above' — the animal soul can dominate, but the divine soul can never be destroyed or removed.
מִכָּל מָקוֹם, שֹׁרֶשׁ כָּל הַנֶּפֶשׁ רוּחַ וּנְשָׁמָה כּוּלָּם, מֵרֹאשׁ כָּל הַמַּדְרֵיגוֹת עַד סוֹף כָּל דַּרְגִין, הַמְלוּבָּשׁ בְּגוּף עַמֵּי הָאָרֶץ וְקַל שֶׁבְּקַלִים, נִמְשָׁךְ מִמּוֹחַ הָעֶלְיוֹן, שֶׁהִיא חָכְמָה עִילָּאָה כִּבְיָכוֹל. וְעִם כָּל זֶה, עוֹדֶינָה קְשׁוּרוֹת וּמְיוּחָדוֹת בְּיִחוּד נִפְלָא וְעָצוּם בְּמַהוּתָן וְעַצְמוּתָן הָרִאשׁוֹן, שֶׁהִיא הַמְשָׁכַת חָכְמָה עִילָּאָה, כִּי יְנִיקַת וְחַיּוּת נֶפֶשׁ רוּחַ וּנְשָׁמָה שֶׁל עַמֵּי הָאָרֶץ, הוּא מִנֶּפֶשׁ רוּחַ וּנְשָׁמָה שֶׁל הַצַּדִּיקִים וְהַחֲכָמִים רָאשֵׁי בְּנֵי יִשְׂרָאֵל שֶׁבְּדוֹרָם:
Nevertheless, the root of every nefesh, ruach, and neshamah, from the highest of all ranks to the lowest that is embodied within the illiterate and the most worthless, all derive, as it were, from the supreme mind which is chochmah ilaah (supernal wisdom). Nevertheless they remain bound and united with a wonderful and essential unity with their original essence and entity; namely, the extension of chochmah ilaah (supernal wisdom), inasmuch as the nurture and life of the nefesh, ruach, and neshamah of the ignorant are drawn from the nefesh, ruach, and neshamah of the saints and sages, the heads of Israel in their generation.