In the end of the play (in my copy of the book, at least) the author gives a brief rundown on what happens to various characters after the play ends.
He does not say for sure what happens to Abigail Williams. However, he does say that "legend" says that she went to Boston and became a prostitute.
I think that he would probably say this because it would seem somewhat just. Since Abigail already more or less sold her soul for revenge and/or power, it is poetic justice, perhaps, that she should end up selling her body too.
The last we hear of Abigail in the text is that she, along with her friend, Mercy Lewis, robbed the Reverend Parris, her uncle, of his life's savings -- thirty one pounds -- and run off to board a ship (as Parris reports to Danforth). Betty Parris heard her cousin and friend discussing ships the week prior, and after Abigail had been missing for a day or two, Parris put two and two together and checked his strongbox. The play gives us no additional clues about where Abigail has gone or what she might be up to.
My text also has an epilogue of sorts, called "Echoes Down the Corridor," which references the Boston prostitute story that others have mentioned. However, history has left no real substantive clues about whatever became of the real Abigail Williams after the trials were over. The real Abigail was eleven years old, not seventeen as she is in the text, and there was no relationship between herself and John Proctor (who was around sixty years old in real life).
After the trials passed Paris was later voted out of office. He disappeared from sight. It was believed that Abigail became a prostitute somewhere in Boston.
The government, about twenty years following all the trials, compensated some of the victims that were alive. Elizabeth Proctor had survived but her husband John had been hung. She married again.
Many of the victims farms had been left to ruin and the cattle ran wild in the state. People did not want to buy them whether it was because they were bad luck or no one wanted to own property gained in such a horrific and unfair way.