The speech closes where it began. Judah returns, at the end, to the same pledge he gave his father at the beginning of the story, and makes it explicit.
"Therefore thy servant became surety for the youth with my father, saying, If I restore him not to thee, let me be guilty before my father all the days" (Genesis 44:32). Targum Pseudo-Jonathan locks the circle shut. The pledge in Genesis 43:9 has become the argument in Genesis 44:32. The vow is not rhetorical. It is operative. It is the ground of everything Judah is about to offer next.
The Aramaic phrase chayav kodam abba kol yomaya — guilty before my father all the days — is the same terminology of unlimited surety used earlier. The word kol yomaya is crucial. Not for a while. Not until the matter is settled. Forever.
Judah is telling the vizier: I have staked my eternity on Benjamin. My father already lost one son. He will not lose this one. If he loses this one, I am the one who lives every remaining day under a curse — in this world and the world to come. So let me, your servant, stay here in Egypt instead, and let the boy go up to his father.
The sages see in this moment the birthright of kingship. Judah does not yet wear a crown. David will not be born for centuries. But the kingship of Israel begins right here, because kingship in the Jewish tradition is not privilege — it is the willingness to step between danger and your people, permanently.
Joseph listens. The cord holding his secret snaps. He clears the room of Egyptians. The next verse will be, I am Joseph.