Does your sister-in-law become your ex-sister-in-law if you are divorced?

Yes; if your sister-in-law is the sister of your spouse, when you divorce your spouse she becomes your ex-sister-in-law. Unless you marry her. Then she becomes your wife.

On the other hand, if your sister-in-law is the wife of your brother, her status has nothing to do with your marital status, but she would become your ex-sister-in-law if she and your brother divorced.