We had a somewhat similiar situation with my family. We had someone that was renting a condo from us. This was someone we like and trust. Long story short, though, she was supposed to have the condo on the market to sell. She wasn't doing that. So we had to go ahead and put it on the market ourselves. Not long ago, it did sell. And the lady had to move out.
I asked my parents just this past weekend where she went. They said that they think she went to live near her son. But that it's really not their concern. There was a deadline, she moved out, and where she went at that point was up to her.
This is someone we like. So it's not just a situation that occurs with a person like the OP and her boarder where there are problems. Once a resident in your home, condo, whatever leaves, where they go isn't the other person's business.