What compromise or deal does Danforth offer Proctor in The Crucible?
It is helpful if you cite a particular segment of the play when asking questions so we can most accurately assist you.
In the final scene, Danforth and Proctor do quite a bit to try to compromise. In Danforth's eyes, he needs both a verbal and signed confession. He also required that Proctor name names of people he has "seen" with the Devil. Then, he needs the confession posted to document to the public the recorded sin and redemption of a particular sinner. Proctor cannot allow himself to give all of this.
Proctor refuses to give names to Danforth. Then Danforth concedes to just accepting a written confession with Proctor's name attached at the bottom.
Danforth: You will give me your honest confession in my hand, or I cannot keep you from the rope.
Here, Danforth is no longer asking for others names, so audience members can assume that Danforth will be justifiably satisfied with just Proctor's signature and then he can live.