At the end of The Crucible, the court officials bring out Elizabeth, hoping that she will plead iwth her husband to confess, so that he won't hang. They hope that Proctor's confession will prompt other prominent figures in the town to confess also, because the officials fear that if Proctor, Rebecca Nurse, and Marth Corey all hang, the townspeople will turn against them, riot, or overthrow the courts. They hope that Proctor's confession will start a chain reaction of confessions that will hopefully maintain their authority.
Unfortunately for them, Elizabeth refuses to make any promises about getting John to confess; instead, she asks to speak to him. In a frank, touching and very emotional conversation between the two, John decides that he will confess in order to save his life. However, once the officials of the court ask him to sign a confession to be nailed on the church door, and to name other friends that were also supposedly witches, he backs out of his confession, takes it back, and refuses to do what they want him to. He ends up going to the gallows and hanging. Elizabeth did not protest; she wanted him to do what he felt was right, and felt, instinctively, that his deicsion finally gave him the confidence and redemption that he needed. So, she doesn't call out or protest, but lets him choose to die--even though it must have been very hard for her.
The question of whether she should have let him hang or not is an interesting one. First of all, she did not have the authority to make that decision for him. Sure, she could have influenced him in that direction, but that was not her style. She realized that if she did "force" him to confess and live, that he would have been a shell of a man who was ashamed of himself for the rest of his life. So, she let him make his own choice, keep his dignity, preserve their family's reputation of integrity and honesty, and she supported him in that choice. I think it was the harder choice to make, and honestly, the better one.
I hope that those thoughts help to clear up any confusion that you might have on the issue. Good luck!