Commentary for Kiddushin 31:7
מסתברא שטר ה"ל לרבויי שכן מוציאה בבת ישראל אדרבה חזקה ה"ל לרבויי שכן קונה בנכסי הגר באישות מיהת לא אשכחן אי בעית אימא להכי אהני אם אחרת
Then say: Only they [are acquired] by deed, but not another? - But it is written, she shall not go out as menservants do.<span class="x" onmousemove="('comment',' From which it was deduced that she can be acquired by deed.');"><sup>10</sup></span> And why do you prefer it so?<span class="x" onmousemove="('comment',' Lit., 'what (reason) do you see' (for interpreting it thus) ? Perhaps Lev. XXV, 46 teaches, only they are acquired by deed, but not another, while Ex. XXI, 7 intimates, she shall not go out . . but may he acquired as menservants, viz., by hazakah?');"><sup>11</sup></span> - It is logical that 'deed' is included [as a means of acquisition], since it divorces an Israelite daughter.<span class="x" onmousemove="('comment',' Hence, just as it is effective in one instance, so also in another, viz., the acquisition of a slave. - Tosaf.: he could also have said: Because it brings a Jewish daughter into the married state, which is more appropriate, both then referring to acquisition, but a 'deed' is explicitly stated in connection with divorce. A proselyte who dies without Jewish issue has no legal heirs and his property after death falls to the first occupier by means of hazakah.');"><sup>12</sup></span>
Daf Shevui to Kiddushin
But then we’d still need to account for the verse that distinguishes how female Jewish slaves go free and how non-Jewish slaves go free. This verse implied that they can all be acquired in the same way. So we have one verse that draws a distinction between them and one that compares them (in terms of acquisition).
So why say that the distinction is made in acquisition through hazakah and that they are both acquired by a document? Why not the opposite?
The answer is that a document has greater power since it is used for divorce.
But still, we could argue, that hazakah has greater power because it can be used to acquire the property of a convert who dies without heirs.
Still, we do not find a case where hazakah (possession) acquires in a case of marriage. And since acquisition of a female slave is somewhat similar to marriage, we can conclude that it does not work in this case. We could also prove that the comparison is only made with regard to rules connected to marriage because the very next verse in Exodus to marriage.
[I realize, this is complicated. Kol Hakavod if you made it through!]