If a woman who wants a divorce destroys her ketubah is she somehow forcing her husband's hand?

Question

Not a practical question! I'm reading a parable (from haza"l) that I don't understand.

If a woman wanted to get out of a marriage because she committed adultery and the choice was between divorce or death (as we see, for instance, in the life of Hosea). Is there some way in which destroying the ketubah would help her force the issue in favor of divorce? Is she somehow making the kiddushin unproveable? Is she forcing her husband to divorce her because he can't sleep with her? (Though she's already forbidden to him because of the adultery.) Is there something that would prevent him from writing a new ketubah and then insisting on the death penalty?

I realize that question mixes up rabbinic and biblical law. I'm trying to understand how the rabbis who wrote a particular allegory would have understood the halacha in a(n imaginary) world in which capital punishment was still in force but ketubah was already a reality.

I'm primarily interested in the question as described above. But if anyone would like to know what brought it to mind: Jacob Neusner/Louis Epstein both suggest that tosefta Bava Kamma 7:4 and parallels compares the first tablets to a ketubah and the second tablets to a get. If you went with this reading, then you would read the smashing of the first tablets as Moshe's attempt to force the issue in favor of divorce over the death penalty (https://books.google.com/books?id=zuxMLzsCrF0C&lpg=PA8&ots=fqU_ZZ7qZC&dq=destroy%20ketubah%20evidence%20of%20marriage&pg=PA8#v=onepage&q=destroy%20ketubah%20evidence%20of%20marriage&f=false). I realize this interpretation of the story is odd. But I'm less interested in the story itself than in why anyone would read it like that.

Related but not identical:

What is the status of a married woman without a kesuba?

Is marriage without ketubah considered marriage, concubinage, or kiddushin she’einah re’uyah le’biah (marriage that cannot be consummated)?

May a woman who has had an affair remain married to her husband?

Answer 1

Kiddushin (technical marriage) is independent of Ketuba. The mishna in Kiddushin said that, after the Kiddushin, she gets out of marriage by Get (bill of divorce) or death of the husband.

Ketuba is a written contract (Kettuba may be translated by written).

Gemara in Ketubot says that there were communities that did not write a Ktuba.

The lack of a written Ketuba may be a proof that the divorced husband already paid it. But if the husband has not divorced, it is more complex.

Anyway, the act of tearing the Ketuba is not in itself a cancellation of nothing (fairly sure, there is a great complexity in halacha concerning the true nature of a Shtar (written legal act), but Shtar Ktuba does not interfer with kiddushin, the fact of being married) but absence of Ketuba can have a marked effect in case of dispute concerning its payment.