For Kesuvos 12b you have the following:
>> (c) The SHAV SHMAISA himself (1:24) writes that perhaps a Sfek Sfeika can be used to collect money only in the case of a Kesuvah. The HAGAHOS MORDECHAI (in Yevamos) writes that since the Kesuvah is already written in a contract, we may follow a "Rov" to collect the money, since it is "k'Man d'Gabuy Dami" -- it is as though it has already been collected, since the woman is holding the contract of the Kesuvah. Therefore, it can be collected through a "Rov,"
since it is not considered to be taking money out of someone else's possession. He adds that since the Kesuvah is an act of Beis Din, it is considered as though the woman is already holding the money, and thus she is not taking it away from him with a "Rov," but the "Rov" is just allowing her to hold on to it. <<
If a woman's kesuba is "K'man d'Gabuy Dami" then why does that same gemorah (12b) assume that he is the "muchzuk" on the money and she is the "Motzei May'chavero"?
In the case on 9b, the woman stands to lose her Kesuvah if the act was done "Tachtav b'Ratzon." She therefore definitely had a Kesuvah and the only question is did she forfeit it. She is therefore considered to be the Muchzak if "k'Man d'Gabuy." In contrast, on 12b the question is whether she was ever entitled to a Kesuvah in the first place (Ad Shelo Arastich), and, therefore, he is considered to be the Muchzak.
D. Zupnik