When a couple gets married, a ketuba – the agreement that is signed by witnesses delineating the obligations that the husband has towards his wife – is written. When the Mishna on our daf refers to the ketuba, it means specifically the monetary responsibilities that the husband has accepted in this relationship, and, in particular, the amount of money that he guaranteed to her in the event of divorce or death.
It was traditional for the wife to also bring financial assets into the marriage, which were divided into two –
Nikhsei melug, which are possessions that remain the property of the woman. While the couple is married, the husband can derive benefit from this property. When the marriage ends, they remain hers, in whatever condition they may be.
Nikhsei tzon barzel, which are possessions that become the property of the husband. Their value is written into the ketuba, and in the event that their marriage comes to an end – if the husband dies or if they become divorced – the wife will be reimbursed for the full amount, either from the estate if he died or from him if they divorced.
Beit Shammai rules that it is divided between her husband’s relatives and her father’s relatives. According to most rishonim, Beit Shammai believes that as a potential yevama, the woman’s relationship with the family is one of safek – of questionable marriage. Thus we are not sure what to do and divide it in half.
Beit Hillel rules that given the questionable situation, we leave the status quo. Thus, the nikhsei tzon barzel remain in the possession of her father, the ketuba remains with the husband’s family, and the nikhsei melug are divided between the two.