No source material left but continues? First time I've seen it happen unless it became a big deviation upfront to the point of being more a "parallel universe" than an adaptation
Fullmetal alchemist the first season and Soul Eater are both examples of series catching up and overtaking the source materials and doing their own thing. Granted in both their case it was the anime that overtook the source but I would have to assume those are not the only ones. Those could be the examples you are referring to with the parallel universe comment since you didn't name them I was not sure.
Three ways forward in my opinion
1. The original author is involved in this project and the story goes on as he or she had in mind.
2. A new author continues the story. We will see how that turns out. Could be good depending on the competence of the author.
3. They rush to an ending. As in the royal capital arc is the last arc.