The first mishnayos of Kidushin, in Sefaria's Silverstein translation, bracketed remarks omitted:
A woman is acquired in three ways, and she acquires herself in two ways. She is acquired by money, by writ, and by cohabitation.... And she acquires herself with a get and with the death of her husband.
A yevamah is acquired by cohabitation, and she acquires herself with chalitzah and with the death of the yavam.
A Hebrew bondsman is acquired by money and by writ. And he acquires himself with years, and with the Jubilee (yovel), and with monetary deduction. The Hebrew handmaid, in addition, acquires herself with signs. A "bored" bondsman is acquired by boring (of the ear), and he acquires himself with yovel and with the death of the master.
A Canaanite bondsman is acquired by money, writ, and chazakah (proprietary act). And he acquires himself by money..., and by a writ (of manumission)....
Something is funny here.
In most of these cases, the "acquires himself" is a reversal of the "is acquired". A woman becomes a wife through money, and thereafter loses that wifehood through a get (bill of divorce). A Jewish servant becomes such by the transfer of money, and thereafter leaves servitude by the passage of years.
But for a y'vama, it's different. This is someone whose husband died childless and who therefore should marry his brother. That marriage is effected, as the mishna notes, through intercourse. And it thereafter ends — well, through a get or the death of the new husband. Chalitza doesn't end the marriage: it ends the half-married state that the woman is in immediately after her husband dies. Listing it in parallel to the other "acquires himself"s is misleading; why does the mishna do it? I'd think it would say she acquires herself through get or the husband's death.