Building on someone else's work

I have an idea for a story, but it's not original. It builds on someone else's unfinished work, which has been untouched for years. I want to make some changes to the story line, but use characters and situations from the source. And yes, I would credit the author of the source material.

Is this a taboo, or something others have done before? If I thought the author would continue the work, I'd leave it alone. But I feel that it is "abandoned" and I want to salvage it, if that makes sense? Is this a bad idea, or should I pursue it?