Proctor offers a false confession in the final act of the play. His hope is to save his life so that his children will have at least one parent. (Elizabeth is sentenced to be killed after she gives birth.)
This is the final compromise that Proctor is willing to make. When he is pressed to sign a confession, going beyond his verbal confession, he balks. Danforth wants to know why he will confess aloud but not on paper.
Proctor breaks out in anger.
"Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang!"
A part of his character cannot accept the shame of this lie, though it will save his life. From this point forward, having been pushed too far, Proctor gropes his way back toward a hard-fought pride. He is unwilling to sully the names of those others that will hang if he signs the confession. He finds also that he has some attachment to a sense of honor that he cannot escape or cast off.
There is no way for him to live without his name, his pride and his honor.
Proctor wordlessly tears up his confession, consigning himself to be hanged.