Judah and his brothers come before Joseph and fall before him on the ground. Joseph is direct: "What deed is this you have done? Do you not know that a man like me can certainly practice divination?" Judah does not argue innocence. He says: "What shall we say to my lord? What shall we speak? Or how can we clear ourselves? God has found out the guilt of your servants." He does not name which guilt — the cup or the old one. The Hebrew word he uses: עֲוֹן — iniquity, moral guilt. The man who sold Joseph is standing before Joseph confessing guilt with the vocabulary of the soul.
Joseph offers a clean exit: only the man in whose possession the cup was found shall be my servant. The rest of you — go in peace to your father. This is the moment. Benjamin stays. All the other brothers can leave. Then Judah steps forward and speaks the longest speech by any human character in Genesis. He retells the entire story from Jacob's reluctance to send Benjamin, to Judah's own pledge, to what it would do to Jacob to lose another son. He is not making a legal argument. He is making a human one. He is speaking to whatever humanity is in this governor — not knowing it is his own brother.
The climax: "Now therefore, please let your servant remain instead of the boy as a servant to my lord, and let the boy go back with his brothers. For how can I go back to my father if the boy is not with me? I fear to see the evil that would find my father." Judah offers himself as a slave. Not his sons (Reuben). Not an argument (the brothers in Egypt). Himself. The man who once said "What profit is it if we kill our brother and conceal his blood?" now stands in Egypt offering to become a slave in Benjamin's place. This is the answer to Joseph's test. It is also the answer to twenty years of waiting. Joseph cannot restrain himself.