So what do we think she did after throwing the address ...

I'd like to think she memorized the address and was off to visit Mr. Madden – and that they ended up spending their lives happily together.

But, like you, I got the sense that we, the audience, were supposed to believe that by throwing the address away, Judith was taking a defiant stand against the people of her past whom she was hurt by. It was her way of being strong. Though, I think the smarter move would've been for her to go with him. Maybe she eventually did – and they lived happily ever after :-)

Please excuse typos/funny wording; I use speech-recognition that doesn't always recognize!